objective: solve word problems involving uniform motion motion in opposite directions

OBJECTIVE: SOLVE WORD

PROBLEMS INVOLVING UNIFORM MOTION

Motion in Opposite Directions

Uniform Motion

Moving at a speed that is not changing.

Distance = Rate x Time

D = RT (dirt)Rate x Time = Distance

50mph x 2hours = 100miles

D/T = RDistance / Time = Rate

100miles / 2hours = 50mph

Distance = Rate x Time

D/R = TDistance /Rate = Time

100miles / 50mph = 2hours

Solving Word Problems

1. Draw a sketch 2. Identify Unknowns3. Assign Variable4. Make a Chart5. Write and solve an equation

Equation for Motion in Opposite Directions

Add distance for both objects and set equal to the total distance apart.

Example Bike riders Brent and Jane started at noon from points 60 km apart and rode toward each other, meeting at 1:30pm. Brent’s speed was 4km/h greater than Jane’s speed.

Find their speeds.

Start riding at 12pm & meet at 1:30pm

Unknown

Jane and Brent’s speed.

Variables

Let r = Jane’s rateLet r + 4 = Brent rate

Make a chart and use the information to label your diagram

Chart

BIKE RIDINGBIKE RIDING RATERATE TIMETIME DISTANCEDISTANCE

JANEJANE

BRENTBRENT

Equation

1.5 ( r + 4) + 1.5r = 60r = 18 Jane’s speedr + 4 = 22 Brent’s speed

Brent’s speed was 22km/h and Jane’s speed was 18 km/h

Try ThisAt noon a private plane left Austin for Los Angeles, 2100km away, flying at 500 km/h. One hour later a jet left Los Angeles for Austin at 700km/h. At what time did they pass each other?

2100 km

500 km

700 km

500t + 700(t – 1) = 2100

TRAVELTRAVEL RATERATE TIMETIME DISTANCEDISTANCE

PLANEPLANE

JETJET

500

700

t

1t

500t

700( 1)t

500t + 700(t – 1) = 2100

500t +700t – 700 = 2100

1200t – 700 = 2100

+700 =+700

1200t = 2800

1200t/1200 =2800/1200

T=2 and 400/1200 HRS or 2 and 1/3hrs is 2hrs 20min

WHATS THE QUESTION Airplane took 2 hours and 20 min before meeting with

Jet that took t – 1 =2hr 20 min – 1 = 1hr and 20 min

Time is 12:00 + 2 hr and 20 min . They jet passed the plane at 2:20