53.5k views
5 votes
Sarah and John are running clockwise around a circular track with radius 25 meters. They start at the same position, and Sarah runs at 2.7 m/s while John runs at 2.2 m/s. How far away from their starting point are they when Sarah catches up and passes John for the first time after the start?

User MoLow
by
8.8k points

1 Answer

3 votes

Answer:

62.8 m

Explanation:

The length of one lap is ...

C = 2πr = 2π(25 m) = 50π m ≈ 157.08 m

Sarah is gaining ground on John at the rate of 2.7 m/s -2.2 m/s = 0.5 m/s. So it will take Sarah ...

157.08 m/(0.5 m/s) = 314.16 s

to run 1 lap farther than John does.

It takes Sarah ...

157.08 m/(2.7 m/s) = 58.18 s

to run 1 lap, so in the time it takes her to catch John, she will have run ...

314.16 s/(58.18 s/lap) = 5.4 laps

She (and John) will be 0.4 laps from their start when they meet again. That distance is ...

(0.4)(157.08 m) = 62.8 m

Sarah will catch and pass John 62.8 meters from their starting position.

Sarah and John are running clockwise around a circular track with radius 25 meters-example-1
User Pepak
by
8.3k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories