OBJECTIVESOLVE PROBLEMS

INVOLVING UNIFORM MOTION

Uniform Motion Round Trip

Uniform Motion

Uniform motion is when an object moves without changing its speed.

Solving Word Problems

1. Draw a sketch 2. Identify unknowns3. Assign variable4. Make a chart5. Write and solve an equation

Equation for Motion Round Trip

Distance for object one equals the distance for object two.

Example

A ski lift carried Maria up a slope at the rate of 6 km/h, and she skied back down parallel to the lift at 34 km/h. The round trip took 30 min.

How long did she ski?

Draw a sketchDraw a Diagram

Assign Variables

Let t = Maria’s skiing time

Notice that 30 min = ½ hour

Make a ChartSKIINGSKIING RATERATE TIMETIME DISTANCEDISTANCE

UPUP

DOWNDOWN

30 t 6 30 t6

34tt34

34 6 30t t

34 180 6t t 6t 6t

40t 40

180

40

20 14 min 4 min40 2

t

Maria skied for 4.5 minutes downhill.She went up the lift for 30-4.5 or 25.5 minutes.How far did she ski? Oh ohSince km/h is in hours 4.5min=__hrsSmall to big divide. 4.5/60=3/40hours3/40hr x 34km/h =2 and 11/20km

Try This

Kathy hiked up a hill at 4 km/h and back down at 6km/h. His total hiking time was 3 hours.

How long did the trip up hill take him?

Make a ChartHIKINGHIKING RATERATE TIMETIME DISTANCEDISTANCE

UPUP

DOWNDOWN

4(3 )t4

6t6

3 t

t

6 4(3 )t t

4t 4t10 12t

10 12

10 10

t

6 11 1 12min

5 5t hr

10 12t

Kathy hiked down the hill for 1 hr 12 min.How long did the trip up take her? Since She went up the hill for 3 hrs - 1 hr 12min 1 hr 48 min minutes