8/14/2019 Lesson: Trains Crossing in the Night Problems

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8/14/2019 Lesson: Trains Crossing in the Night Problems

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• From the time Patricia leaves, model exactly how far apart they are after any number of hours (h) on agraph. Can you include an equation or two equations to fit the graph?

h

      D     i    s     t    a    n    c    e    a    p    a    r     t

• From the time Patricia leaves, how many hours until they are 200 miles apart? (Round to the nearestHundredth)

• From the time Holly leaves, how many hours until they are 300 miles apart?

Objects Chasing Each Other

1. A chases B. B has a head start of 2 minutes and goes 30 miles per hour. A will go 40 miles per hour.

• How long after they start will A catch B?

• How far will they both have travelled?

2. Adele runs down the soccer field at a clip, 11 miles per hour. She’s chasing an opponent, with the ball (thoughnot for long), who’s running at 8 miles per hour. If her opponent is 30 feet ahead of her, will she reach heropponent before her opponent runs 50 yards?

Challenge

1. Rafters travelling on a river can row the raft 5 miles per hour relative to the water. If the water is travelling10 miles per hour, how long will it take the rafters to float 1 mile? How much of that mile will the rafters havecoasted through and how much did they feel like they rowed?

8/14/2019 Lesson: Trains Crossing in the Night Problems

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Solutions

Ships Passing. . . in the night

1. 261

4hours

2. 100 miles from Miami

3. 54 crosses. (4 + 2) · 60 · 60 = 21600, so together the runners will cover that many meters in an hour. Every 400meters they will cross paths, so they should cross 54 times.

Objects Moving Away from Each Other

1. 40 seconds

2. 0 1 2 3 40

50

100

150

h

      D     i    s     t    a    n    c    e    a    p    a    r     t

   

d = 68h

d = 136 + 131(h− 2)

• From the time Patricia leaves, it wil be ≈ 2.49 hours, or 2 hours and 29.31 minutes (rounding to the

nearest hundredth) until they are 200 miles apart.• From the time Holly leaves it will be ≈ 1.25 hours until they are 300 miles apart.

Objects Chasing Each Other

1. • After B starts, it will be 8 minutes until A catches up (6 minutes of travel time for A.

• They will both have travelled 4 miles.

2. Adele has 30 feet to make up, and she gains on her opponent at 3 miles per hour or 3 · 5280 · 1

3600= 4.4

feet

second.

At that rate it will take her 6 9

11seconds to catch her opponent. In that time her opponent who is travelling 8

miles per hour (or 11 11

15

feet

secondwill cover 80 feet, which is 26 2

3yards, so yes, Adele will reach her opponent

before her opponent runs 50 yards.

Challenge

1. It will take the rafters 1/15th of an hour, 4 minutes, to float 1 mile. The rafters will feel as though they rowed1

3of a mile, and they will have coasted through 2

2of it.