valley county challenge · 2guitars 2apples/orange 61 units of measurement •cannot add or...

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1 [email protected] Valley County Challenge Word Problem of the Week Solution 1 The following approach is just one of many ways to tackle the word problem 2 Airplane Fuel 3

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Page 1: Valley County Challenge · 2guitars 2apples/orange 61 Units of Measurement •Cannot add or subtract different units •Can treat units like numbers and variables when multiplying

1

[email protected]

Valley County Challenge

Word Problem of the Week

Solution

1

The following approach is just one ofmany ways to tackle the word problem

2

Airplane Fuel

3

Page 2: Valley County Challenge · 2guitars 2apples/orange 61 Units of Measurement •Cannot add or subtract different units •Can treat units like numbers and variables when multiplying

2

[email protected]

Airplane Fuel

4

Knowns

• Home airport to an airstrip 40 minutes away in cruise flight, then return home

Key Info

5

Preliminary Sketch

Drawing

HomeAirport

BackcountryAirstrip

Top View

Leg 1

Leg 2

Not to scale

40 minutes

6

Page 3: Valley County Challenge · 2guitars 2apples/orange 61 Units of Measurement •Cannot add or subtract different units •Can treat units like numbers and variables when multiplying

3

[email protected]

Knowns

• Home airport to an airstrip 40 minutes away in cruise flight, then return home

• 30-minute fuel reserve

• Taxi, takeoff, and climb will use 23 pounds of fuel

• Cruise will use 78 pounds of fuel per hour

• Descent, landing, and taxi will use 11 pounds of fuel

Key Info

7

Preliminary Sketch

Drawing

Not to scale

Taxi Taxi

Cruise

LandingClimb Descent

Takeoff Profile View(per leg)

HomeAirport

BackcountryAirstrip

Top View

Leg 1

Leg 2

40 minutes

8

Knowns

• Home airport to an airstrip 40 minutes away in cruise flight, then return home

• 30-minute fuel reserve

• Taxi, takeoff, and climb will use 23 pounds of fuel

• Cruise will use 78 pounds of fuel per hour

• Descent, landing, and taxi will use 11 pounds of fuel

• Fuel weighs six pounds per gallon

Key Info

9

Page 4: Valley County Challenge · 2guitars 2apples/orange 61 Units of Measurement •Cannot add or subtract different units •Can treat units like numbers and variables when multiplying

4

[email protected]

Knowns

• Home airport to an airstrip 40 minutes away in cruise flight, then return home

• 30-minute fuel reserve

• (Taxi, takeoff, and climb) will use 23 pounds of fuel

• Cruise will use 78 pounds of fuel per hour

• (Descent, landing, and taxi) will use 11 pounds of fuel

• Fuel weighs six pounds per gallon

Key Info

10

Substitutions

• (Taxi, takeoff, and climb)

• Cruise

• (Descent, landing, and taxi)

Combine and Abbreviate

11

Substitutions

• Takeoff

• Cruise

• Landing

Combine and Abbreviate

Nouns

• Takeoff as T

• Cruise as C

• Landing as L

12

Page 5: Valley County Challenge · 2guitars 2apples/orange 61 Units of Measurement •Cannot add or subtract different units •Can treat units like numbers and variables when multiplying

5

[email protected]

Rewrite

Knowns

• Home airport to an airstrip 40 minutes away in cruise flight, then return home

• 30-minute fuel reserve

• (Taxi, takeoff, and climb) will use 23 pounds of fuel

• Cruise will use 78 pounds of fuel per hour

• (Descent, landing, and taxi) will use 11 pounds of fuel

• Fuel weighs six pounds per gallon

13

Rewrite

Knowns

• Home airport to an airstrip 40 minutes away in cruise flight, then return home

• 30-minute fuel reserve

• T will use 23 pounds of fuel

• C will use 78 pounds of fuel per hour

• L will use 11 pounds of fuel

• Fuel weighs six pounds per gallon

14

Rewrite

Knowns

• Home airport to an airstrip 40 minutes away in cruise flight, then return home

• 30-minute fuel reserve

• T will use 23 pounds of fuel

• C will use 78 pounds of fuel per hour

• L will use 11 pounds of fuel

• Fuel weighs six pounds per gallon

Verbs

15

Page 6: Valley County Challenge · 2guitars 2apples/orange 61 Units of Measurement •Cannot add or subtract different units •Can treat units like numbers and variables when multiplying

6

[email protected]

Rewrite

Knowns

• Home airport to an airstrip 40 minutes away in cruise flight, then return home

• 30-minute fuel reserve

• T will use 23 pounds of fuel

• C will use 78 pounds of fuel per hour

• L will use 11 pounds of fuel

• Fuel weighs six pounds per gallon

Verbs

16

Rewrite

Knowns

• Home airport to an airstrip 40 minutes away in cruise flight, then return home

• 30-minute fuel reserve

• T will use 23 pounds of fuel

• C will use 78 pounds of fuel per hour

• L will use 11 pounds of fuel

• Weight of fuel is six pounds per gallon

Verbs

17

Rewrite

Knowns

• Home airport to an airstrip 40 minutes away in cruise flight, then return home

• 30-minute fuel reserve

• T will use 23 pounds of fuel

• C will use 78 pounds of fuel per hour

• L will use 11 pounds of fuel

• Weight of fuel is six pounds per gallon

Verbs

18

Page 7: Valley County Challenge · 2guitars 2apples/orange 61 Units of Measurement •Cannot add or subtract different units •Can treat units like numbers and variables when multiplying

7

[email protected]

Rewrite

Knowns

• Home airport to an airstrip 40 minutes away in cruise flight, then return home

• 30-minute fuel reserve

• T = 23 pounds of fuel

• C = 78 pounds of fuel per hour

• L = 11 pounds of fuel

• Weight of fuel = six pounds per gallon

“is equal to”

19

Rewrite

Knowns

• Home airport to an airstrip 40 minutes away in cruise flight, then return home

• 30-minute fuel reserve

• T = 23 pounds of fuel

• C = 78 pounds of fuel per hour

• L = 11 pounds of fuel

• Weight of fuel = six pounds per gallon

20

Rewrite

Knowns

• Home airport to an airstrip 40 minutes away in cruise flight, then return home

• 30-minute reserve

• T = 23 pounds

• C = 78 pounds per hour

• L = 11 pounds

• Weight = six pounds per gallon

21

Page 8: Valley County Challenge · 2guitars 2apples/orange 61 Units of Measurement •Cannot add or subtract different units •Can treat units like numbers and variables when multiplying

8

[email protected]

Rewrite

Knowns

• Home airport to an airstrip 40 minutes away in cruise flight, then return home

• 30-minute reserve

• T = 23 pounds

• C = 78 pounds per hour

• L = 11 pounds

• Weight = six pounds per gallonSubstitute “W” for “Weight”

22

Rewrite

Knowns

• Home airport to an airstrip 40 minutes away in cruise flight, then return home

• 30-minute reserve

• T = 23 pounds

• C = 78 pounds per hour

• L = 11 pounds

• W = six pounds per gallon

23

Rewrite

Knowns

• Home airport to an airstrip 40 minutes away in cruise flight, then return home

• 30-minute reserve

• T = 23 pounds

• C = 78 pounds per hour

• L = 11 pounds

• W = six pounds per gallon

24

Page 9: Valley County Challenge · 2guitars 2apples/orange 61 Units of Measurement •Cannot add or subtract different units •Can treat units like numbers and variables when multiplying

9

[email protected]

Rewrite

Knowns

• Home airport to an airstrip 40 minutes away in cruise flight, then return home

• 30-minute reserve

• T = 23 pounds

• C = 78 pounds per hour

• L = 11 pounds

• W = 6 pounds per gallon

25

Rewrite

Knowns

• Home airport to an airstrip 40 minutes away in cruise flight, then return home

• 30-minute reserve

• T = 23 pounds

• C = 78 pounds per hour

• L = 11 pounds

• W = 6 pounds per gallon

from the

Latin “libra”

Abbreviate as “lb”

26

Rewrite

Knowns

• Home airport to an airstrip 40 minutes away in cruise flight, then return home

• 30-minute reserve

• T = 23 lb

• C = 78 lb per hour

• L = 11 lb

• W = 6 lb per gallon

27

Page 10: Valley County Challenge · 2guitars 2apples/orange 61 Units of Measurement •Cannot add or subtract different units •Can treat units like numbers and variables when multiplying

10

[email protected]

Rewrite

Knowns

• Home airport to an airstrip 40 minutes away in cruise flight, then return home

• 30-minute reserve

• T = 23 lb

• C = 78 lb per hour

• L = 11 lb

• W = 6 lb per gallon

Mathematically

÷ ∕ —

Means “for each”or “for every”

28

Rewrite

Knowns

• Home airport to an airstrip 40 minutes away in cruise flight, then return home

• 30-minute reserve

• T = 23 lb

• C = 78 lb / hour

• L = 11 lb

• W = 6 lb / gallon

29

Rewrite

Knowns

• Home airport to an airstrip 40 minutes away in cruise flight, then return home

• 30-minute reserve

• T = 23 lb

• C = 78 lb / hour

• L = 11 lb

• W = 6 lb / gallon

Abbreviate as “hr”

Abbreviate as “gal”

30

Page 11: Valley County Challenge · 2guitars 2apples/orange 61 Units of Measurement •Cannot add or subtract different units •Can treat units like numbers and variables when multiplying

11

[email protected]

Rewrite

Knowns

• Home airport to an airstrip 40 minutes away in cruise flight, then return home

• 30-minute reserve

• T = 23 lb

• C = 78 lb / hr

• L = 11 lb

• W = 6 lb / gal

31

Rewrite

Knowns

• Home airport to an airstrip 40 minutes away in cruise flight, then return home

• 30-minute reserve

• T = 23 lb

• C = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

32

Rewrite

Knowns

• Home airport to an airstrip 40 minutes away in cruise flight, then return home

• 30-minute reserve

• T = 23 lb

• C = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

Different Units

of Measurement

33

Page 12: Valley County Challenge · 2guitars 2apples/orange 61 Units of Measurement •Cannot add or subtract different units •Can treat units like numbers and variables when multiplying

12

[email protected]

Rewrite

Knowns

• Home airport to an airstrip 40 minutes away in cruise flight, then return home

• 30-minute reserve

• T = 23 lb

• C = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

Special Ratios called “Rates”

34

Rates

Numerators and denominatorsof different units

Special Ratios

numerator/denominator numeratordenominator

35

Rates

Miles per hour

distancetimespeed =

“Rate of change of distance with time”

36

Page 13: Valley County Challenge · 2guitars 2apples/orange 61 Units of Measurement •Cannot add or subtract different units •Can treat units like numbers and variables when multiplying

13

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Rates

Sales Tax

“Sales tax rate is 8%”

taxsubtotal% = ×100

37

Rewrite

Knowns

• Home airport to an airstrip 40 minutes away in cruise flight, then return home

• 30-minute reserve

• T = 23 lb

• C = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

38

Knowns

• Home airport to an airstrip 40 minutes away in cruise flight, then return home

• 30-minute reserve

• T = 23 lb

• C = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

Rewrite

39

Page 14: Valley County Challenge · 2guitars 2apples/orange 61 Units of Measurement •Cannot add or subtract different units •Can treat units like numbers and variables when multiplying

14

[email protected]

Rewrite

Knowns

• Leg 1 40 minutes away in cruise flight, then return home

• 30-minute reserve

• T = 23 lb

• C = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

40

Rewrite

Knowns

• Leg 1 40 minutes away in cruise flight, then return home

• 30-minute reserve

• T = 23 lb

• C = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

41

Rewrite

Knowns

• Leg 1 40 minutes away in cruise flight, Leg 2

• 30-minute reserve

• T = 23 lb

• C = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

42

Page 15: Valley County Challenge · 2guitars 2apples/orange 61 Units of Measurement •Cannot add or subtract different units •Can treat units like numbers and variables when multiplying

15

[email protected]

Rewrite

Knowns

• Leg 1 40 minutes away in cruise flight, Leg 2

• 30-minute reserve

• T = 23 lb

• C = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

Each leg takes 40 minutes!

43

Rewrite

Knowns

• 40 minutes per leg in cruise flight

• 30-minute reserve

• T = 23 lb

• C = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

44

Rewrite

Knowns

• 40 minutes per leg in cruise flight

• 30-minute reserve

• T = 23 lb

• C = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

Substitute “C” for “cruise”

45

Page 16: Valley County Challenge · 2guitars 2apples/orange 61 Units of Measurement •Cannot add or subtract different units •Can treat units like numbers and variables when multiplying

16

[email protected]

Rewrite

Knowns

• C = 40 minutes per leg

• 30-minute reserve

• T = 23 lb

• C = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

46

Rewrite

Knowns

• C = 40 minutes per leg

• 30-minute reserve

• T = 23 lb

• C = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

Different Units

47

Rewrite

Knowns

• C = 40 minutes per leg

• 30-minute reserve

• T = 23 lb

• C = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

Clarify “C” with “Ct”

Clarify “C” with “Cf”

48

Page 17: Valley County Challenge · 2guitars 2apples/orange 61 Units of Measurement •Cannot add or subtract different units •Can treat units like numbers and variables when multiplying

17

[email protected]

Rewrite

Knowns

• Ct = 40 minutes / leg

• 30-minute reserve

• T = 23 lb

• Cf = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

49

Rewrite

Knowns

• Ct = 40 minutes / leg

• 30-minute reserve

• T = 23 lb

• Cf = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

Abbreviate as “min”

50

Rewrite

Knowns

• Ct = 40 min / leg

• 30 min reserve

• T = 23 lb

• Cf = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

51

Page 18: Valley County Challenge · 2guitars 2apples/orange 61 Units of Measurement •Cannot add or subtract different units •Can treat units like numbers and variables when multiplying

18

[email protected]

Rewrite

Knowns

• Ct = 40 min/leg

• 30 min reserve

• T = 23 lb

• Cf = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

This is also a Rate!

52

Rewrite

Knowns

• Ct = 40 min/leg

• 30 min reserve

• T = 23 lb

• Cf = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

Substitute “R t” for fuel “reserve time”

53

Rewrite

Knowns

• Ct = 40 min/leg

• Rt = 30 min

• T = 23 lb

• Cf = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

54

Page 19: Valley County Challenge · 2guitars 2apples/orange 61 Units of Measurement •Cannot add or subtract different units •Can treat units like numbers and variables when multiplying

19

[email protected]

Rewrite

Knowns

• Ct = 40 min/leg

• Rt = 30 min

• T = 23 lb

• Cf = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

55

Airplane Fuel

56

Airplane Fuel

57

Page 20: Valley County Challenge · 2guitars 2apples/orange 61 Units of Measurement •Cannot add or subtract different units •Can treat units like numbers and variables when multiplying

20

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Unknowns

• How many gallons of fuel does the pilot need?

Rewrite

58

Unknowns

• How many gallons of fuel does the pilot need?

Rewrite

Final units must be “gal”

59

Unitsof

Measurement Modifiers

Units give numbers character

2 abstract

60

Page 21: Valley County Challenge · 2guitars 2apples/orange 61 Units of Measurement •Cannot add or subtract different units •Can treat units like numbers and variables when multiplying

21

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Unitsof

Measurement 2 dollars

2 guitars

2 apples/orange

61

Unitsof

Measurement

• Cannot add or subtract different units

• Can treat units like numbers and variables when multiplying or dividing

Caveats

62

Unitsof

Measurement6 lb

hr ×2 = (6×2) lbhr

63

Page 22: Valley County Challenge · 2guitars 2apples/orange 61 Units of Measurement •Cannot add or subtract different units •Can treat units like numbers and variables when multiplying

22

[email protected]

Unitsof

Measurement6 lb

hr ×2 = 12 lbhr

64

Unitsof

Measurement6 lb

hr ×2

6 lbhr ×2 hr

= 12 lbhr

65

Unitsof

Measurement6 lb

hr ×2

= (6×2)( )( )lbhr hr6 lb

hr ×2 hr

= 12 lbhr

66

Page 23: Valley County Challenge · 2guitars 2apples/orange 61 Units of Measurement •Cannot add or subtract different units •Can treat units like numbers and variables when multiplying

23

[email protected]

Unitsof

Measurement6 lb

hr ×2

6 lbhr ×2 hr

= 12 lbhr

= 12( )( )hrlbhr

67

Unitsof

Measurement6 lb

hr ×2

6 lbhr ×2 hr

= 12 lbhr

= 12( )( )lbhr

hr1

68

Unitsof

Measurement6 lb

hr ×2

6 lbhr ×2 hr

= 12 lbhr

= 12( )( )hrhr

lb1

69

Page 24: Valley County Challenge · 2guitars 2apples/orange 61 Units of Measurement •Cannot add or subtract different units •Can treat units like numbers and variables when multiplying

24

[email protected]

Unitsof

Measurement6 lb

hr ×2

6 lbhr ×2 hr

= 12 lbhr

= 12( )( )hrhr

lb1

70

Unitsof

Measurement6 lb

hr ×2

6 lbhr ×2 hr

= 12 lbhr

= 12( )( )lb11

71

= 12

Unitsof

Measurement6 lb

hr ×2

6 lbhr ×2 hr lb

= 12 lbhr

72

Page 25: Valley County Challenge · 2guitars 2apples/orange 61 Units of Measurement •Cannot add or subtract different units •Can treat units like numbers and variables when multiplying

25

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= 12

Unitsof

Measurement6 lb

hr ×2

6 lbhr ×2 hr lb

= 12 lbhr

6 lbhr ×2 hr

73

= 12

Unitsof

Measurement6 lb

hr ×2

6 lbhr ×2 hr lb

= 12 lbhr

6 lbhr ×2 hr = 12 lb

74

Solution

Knowns

• Ct = 40 min/leg

• Rt = 30 min

• T = 23 lb

• Cf = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

Mindful of Units

75

Page 26: Valley County Challenge · 2guitars 2apples/orange 61 Units of Measurement •Cannot add or subtract different units •Can treat units like numbers and variables when multiplying

26

[email protected]

Solution

Knowns

• Ct = 40 min/leg

• Rt = 30 min

• T = 23 lb

• Cf = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

76

Solution

Knowns

• Ct = 40 min/leg

• Rt = 30 min

• T = 23 lb

• Cf = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

77

Knowns

• Ct = 40 min/leg

• Rt = 30 min

• T = 23 lb

• Cf = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

Solution

T C L

78

Page 27: Valley County Challenge · 2guitars 2apples/orange 61 Units of Measurement •Cannot add or subtract different units •Can treat units like numbers and variables when multiplying

27

[email protected]

Knowns

• Ct = 40 min/leg

• Rt = 30 min

• T = 23 lb

• Cf = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

Solution

(T + C + L)leg ×2 legs

79

Knowns

• Ct = 40 min/leg

• Rt = 30 min

• T = 23 lb

• Cf = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

Solution

2(T + C + L)

80

Knowns

• Ct = 40 min/leg

• Rt = 30 min

• T = 23 lb

• Cf = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

Solution

2(T + C + L)

81

Page 28: Valley County Challenge · 2guitars 2apples/orange 61 Units of Measurement •Cannot add or subtract different units •Can treat units like numbers and variables when multiplying

28

[email protected]

Knowns

• Ct = 40 min/leg

• Rt = 30 min

• T = 23 lb

• Cf = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

Solution

2(23 lb + C + 11 lb)

82

Knowns

• Ct = 40 min/leg

• Rt = 30 min

• T = 23 lb

• Cf = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

Solution

2(34 lb + C)

83

Knowns

• Ct = 40 min/leg

• Rt = 30 min

• T = 23 lb

• Cf = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

Solution

2(34 lb + C)

84

Page 29: Valley County Challenge · 2guitars 2apples/orange 61 Units of Measurement •Cannot add or subtract different units •Can treat units like numbers and variables when multiplying

29

[email protected]

Knowns

• Ct = 40 min/leg

• Rt = 30 min

• T = 23 lb

• Cf = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

Solution

2(34 lb + C)

Units of C must be in “lb”

85

Knowns

• Ct = 40 min/leg

• Rt = 30 min

• T = 23 lb

• Cf = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

Solution

2(34 lb + C)

86

Knowns

• Ct = 40 min/leg

• Rt = 30 min

• T = 23 lb

• Cf = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

Solution

2(34 lb + C)Ct and Cf are parts of C

87

Page 30: Valley County Challenge · 2guitars 2apples/orange 61 Units of Measurement •Cannot add or subtract different units •Can treat units like numbers and variables when multiplying

30

[email protected]

Knowns

• Ct = 40 min/leg

• Rt = 30 min

• T = 23 lb

• Cf = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

Solution

2(34 lb + C)minleg and 78 lb

hr40 get us to C in lb

88

Knowns

• Ct = 40 min/leg

• Rt = 30 min

• T = 23 lb

• Cf = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

Solution

2(34 lb + C)minleg40 lb

hr78×

89

Knowns

• Ct = 40 min/leg

• Rt = 30 min

• T = 23 lb

• Cf = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

Solution

2(34 lb + C)minleg

lbhr78)×(40

90

Page 31: Valley County Challenge · 2guitars 2apples/orange 61 Units of Measurement •Cannot add or subtract different units •Can treat units like numbers and variables when multiplying

31

[email protected]

Knowns

• Ct = 40 min/leg

• Rt = 30 min

• T = 23 lb

• Cf = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

Solution

2(34 lb + C)minleg

lbhr3,120

91

Knowns

• Ct = 40 min/leg

• Rt = 30 min

• T = 23 lb

• Cf = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

Solution

2(34 lb + C)minleg

lbhr3,120

60 min = 1 hr or 60 min/hr or hr/60 min

92

Knowns

• Ct = 40 min/leg

• Rt = 30 min

• T = 23 lb

• Cf = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

Solution

2(34 lb + C)minleg

lbhr3,120 hr

60 min

93

Page 32: Valley County Challenge · 2guitars 2apples/orange 61 Units of Measurement •Cannot add or subtract different units •Can treat units like numbers and variables when multiplying

32

[email protected]

Knowns

• Ct = 40 min/leg

• Rt = 30 min

• T = 23 lb

• Cf = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

Solution

2(34 lb + C)minleg

lbhr3,120 hr

60 min

94

Knowns

• Ct = 40 min/leg

• Rt = 30 min

• T = 23 lb

• Cf = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

Solution

2(34 lb + C)lbleg

3,12060

95

Knowns

• Ct = 40 min/leg

• Rt = 30 min

• T = 23 lb

• Cf = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

Solution

2(34 lb + C)lbleg52

96

Page 33: Valley County Challenge · 2guitars 2apples/orange 61 Units of Measurement •Cannot add or subtract different units •Can treat units like numbers and variables when multiplying

33

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Knowns

• Ct = 40 min/leg

• Rt = 30 min

• T = 23 lb

• Cf = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

Solution

2(34 lb + C)lbleg52 = C

97

Knowns

• Ct = 40 min/leg

• Rt = 30 min

• T = 23 lb

• Cf = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

Solution

2(34 lb + C)lbleg52 = C

98

Knowns

• Ct = 40 min/leg

• Rt = 30 min

• T = 23 lb

• Cf = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

Solution

2(34 lb + 52 lb)

99

Page 34: Valley County Challenge · 2guitars 2apples/orange 61 Units of Measurement •Cannot add or subtract different units •Can treat units like numbers and variables when multiplying

34

[email protected]

Knowns

• Ct = 40 min/leg

• Rt = 30 min

• T = 23 lb

• Cf = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

Solution

2(86 lb)

100

Knowns

• Ct = 40 min/leg

• Rt = 30 min

• T = 23 lb

• Cf = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

Solution

2(86 lb)

101

Knowns

• Ct = 40 min/leg

• Rt = 30 min

• T = 23 lb

• Cf = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

Solution

172 lb = Fuel used on round trip

102

Page 35: Valley County Challenge · 2guitars 2apples/orange 61 Units of Measurement •Cannot add or subtract different units •Can treat units like numbers and variables when multiplying

35

[email protected]

Knowns

• Ct = 40 min/leg

• Rt = 30 min

• T = 23 lb

• Cf = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

Solution

172 lb = Fuel used on round trip

+ Fuel Reserve

103

Knowns

• Ct = 40 min/leg

• Rt = 30 min

• T = 23 lb

• Cf = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

Solution

172 lb = Fuel used on round trip

Rt and Cf are part of Fuel Reserve

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Knowns

• Ct = 40 min/leg

• Rt = 30 min

• T = 23 lb

• Cf = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

Solution

172 lb = Fuel used on round trip

min and 78 lbhr30 get us to Fuel Reserve

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Page 36: Valley County Challenge · 2guitars 2apples/orange 61 Units of Measurement •Cannot add or subtract different units •Can treat units like numbers and variables when multiplying

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Knowns

• Ct = 40 min/leg

• Rt = 30 min

• T = 23 lb

• Cf = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

Solution

172 lb = Fuel used on round trip

30 lbhr78×min

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Knowns

• Ct = 40 min/leg

• Rt = 30 min

• T = 23 lb

• Cf = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

Solution

172 lb = Fuel used on round triplbhr78)×(30 min

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Knowns

• Ct = 40 min/leg

• Rt = 30 min

• T = 23 lb

• Cf = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

Solution

172 lb = Fuel used on round triplbhr2,340 min

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Page 37: Valley County Challenge · 2guitars 2apples/orange 61 Units of Measurement •Cannot add or subtract different units •Can treat units like numbers and variables when multiplying

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Knowns

• Ct = 40 min/leg

• Rt = 30 min

• T = 23 lb

• Cf = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

Solution

172 lb = Fuel used on round triplbhr2,340 min hr

60 min

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Knowns

• Ct = 40 min/leg

• Rt = 30 min

• T = 23 lb

• Cf = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

Solution

172 lb = Fuel used on round triplbhr2,340 min hr

60 min

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Knowns

• Ct = 40 min/leg

• Rt = 30 min

• T = 23 lb

• Cf = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

Solution

172 lb = Fuel used on round trip

lb2,34060

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Page 38: Valley County Challenge · 2guitars 2apples/orange 61 Units of Measurement •Cannot add or subtract different units •Can treat units like numbers and variables when multiplying

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Knowns

• Ct = 40 min/leg

• Rt = 30 min

• T = 23 lb

• Cf = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

Solution

172 lb = Fuel used on round trip

39 lb = Fuel reserve

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Knowns

• Ct = 40 min/leg

• Rt = 30 min

• T = 23 lb

• Cf = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

Solution

172 lb Fuel used on round trip39 lb Fuel reserve+

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Knowns

• Ct = 40 min/leg

• Rt = 30 min

• T = 23 lb

• Cf = 78 lb/hr

• L = 11 lb

• W = 6 lb/gal

Solution

172 lb Fuel used on round trip39 lb+

211 lbFuel reserveTotal fuel needed

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Page 39: Valley County Challenge · 2guitars 2apples/orange 61 Units of Measurement •Cannot add or subtract different units •Can treat units like numbers and variables when multiplying

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Solution

Unknowns

• How many gallons of fuel does the pilot need?

Fuel needed = 211 lbW = 6 lb/gal

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Solution

Unknowns

• How many gallons of fuel does the pilot need?

Fuel needed = 211 lbW = 6 lb/gal = gal/6 lb

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Solution

Unknowns

• How many gallons of fuel does the pilot need?

Fuel needed = 211 lbW = 6 lb/gal

gal6 lb×

= gal/6 lb

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Page 40: Valley County Challenge · 2guitars 2apples/orange 61 Units of Measurement •Cannot add or subtract different units •Can treat units like numbers and variables when multiplying

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Solution

Unknowns

• How many gallons of fuel does the pilot need?

Fuel needed = 2116 gal

W = 6 lb/gal = gal/6 lb

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Solution

Unknowns

• How many gallons of fuel does the pilot need?

Fuel needed = 35.2 gal

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Airplane Fuel

Report

Bluebird Aviation operates from one of Valley County’s general aviation airports, transporting people and supplies to Idaho’s backcountry airstrips. With 35.2 gallons of fuel in the tanks, the weight of supplies that can be flown to an airstrip 40 minutes from Bluebird’s home base can be maximized, while providing a 30-minute fuel reserve for safety.

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Page 41: Valley County Challenge · 2guitars 2apples/orange 61 Units of Measurement •Cannot add or subtract different units •Can treat units like numbers and variables when multiplying

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Final Diagram

Drawing

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Animation

Drawing

122

Animation

Drawing

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Page 42: Valley County Challenge · 2guitars 2apples/orange 61 Units of Measurement •Cannot add or subtract different units •Can treat units like numbers and variables when multiplying

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This was one of many ways towork through the word problem

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