8.5 Motion Problems

distance = (rate)(time)

Victor drives 60 miles per hour for 3 hours. How far did he drive?

Elise drives 200 miles in 4 hours. How fast did she drive?

Destiny drives 50 miles per hour and travels 300 miles. How many hours did she drive?

Patterns

• Same direction: subtract

• Opposite directions: add

• Overtake: set distances equal to each other

Fred leaves the school on his bicycle and travels west at 14 km/h. Celia leaves and walks east at 6 km/h. How many hours

does it take for Fred and Celia to be 70 km apart?

70cfd d Fred Celia

6cd x 14fd x

64 701 x x 7 1 3

2 2x or hours

Fred leaves the school on his bicycle and travels west at 15 km/h. Celia leaves and

jogs east at 9 km/h. How many hours does it take for Fred and Celia to be 96 km

apart?

96cfd d Fred Celia

9cd x 15fd x

95 961 x x 4 x hours

Fred leaves the school on his bicycle and travels east at 17 km/h. Celia goes in the same direction at 9 km/h. In how many

hours will they be 96 km apart?

Celia 9cd xFred

17fd x

97 961 x x

12x hours

96

8 96x

Jake leaves the school on his Vespa and travels east at 23 mph. Lisa leaves in the

same direction at 6 mph. How many hours does it take for them to be 68 mi

apart?

Lisa 6cd xJake

23fd x

63 682 x x

4 x hours

68

17 68x

Fred leaves on his bicycle and travels west at 15 km/h. Two hours later Celia jogs east at 9 km/h. How many hours does it

take for them to be 102 km apart?

102cfd d Fred Celia

9 cd x 15fd x

95 2 1021 x x

5 hoursLet x = hours after Fred leaves

15 9 18 102x x

-2

24 120x

Dan leaves the school on his skateboard and travels west at 7 km/h. 3 hours later Brisa jogs east at 8 km/h. In many hours

will they be 81 km apart?

81cfd d Dan Brisa

8 cd x 7fd x

87 18 3x x

7 hoursLet x = hours after Dan leaves

15 24 81x

-3

15 105x

Alex leaves the school on his jetskates and travels west at 25 km/h. 1 hour later Elise skates in the same direction at 7 km/h. In

many hours will they be 88 km apart?

4.5 hours18 81x

Elise

Alex

88

25Nd x

7 Bd x -1

2 9x

25 (x) – 7 (x-1) =8825x -7x +7 =88

A small plane left Chicago at 11:00 p. m. and traveled at 180 mi/h. A jet left Chicago and traveled in the same direction at 720 mi/h. If the jet left Chicago at 2:00 a.m., at what time will the jet overtake the small plane?

smallplane

180x

jet

720 x 3

180 720 2160x x 2160 540x

3 am

4 x

A plane left LAX at noon and traveled at 300 mi/h. A jet left LAX and traveled in the same direction at 700 mi/h. If the jet left at 2:00 pm, at what time will the jet overtake the small plane?

smallplane

300x

jet

700 x 2

300 700 1400x x 1400 400x

3:30 pm

13

2x

Same Direction Video

http://www.youtube.com/watch?v=pX2_JxVRzBM

Opposite Direction Video

http://www.youtube.com/watch?v=_omz6n2UtMA

AssignmentPage 384

4, 5,6, 9, 10, 13, 14