Question

A hare and a tortoise compete in a race over a straight course 0.90 km long. The tortoise crawls at a speed of 0.300 m/s toward the finish line. The hare runs at a speed of 7.90 m/s toward the finish line for 0.720 km and then stops to tease the slow-moving tortoise as the tortoise eventually passes by. The hare waits for a while after the tortoise passes and then runs toward the finish line again at 7.90 m/s. Both the hare and the tortoise cross the finish line at the exact same instant. Assume both animals, when moving, move steadily at their respective speeds.

(a) How far is the tortoise from the finish line when the hare resumes the race?

(b) For how long in time was the hare stationary?

Answer 1

Time taken by tortoise upto finish lane = 0.9*10^3 / 0.3 = 3000 sec

Time taken by hare for 0.72km = 0.72*10^3 / 7.9 = 91.139 s

Time taken by hare from 0.72 to finish line = (0.9-0.72)*10^3 / 7.9 = 22.785 s

a) s = 0.3*22.785 = 6.835 m

b) hare is stationery for time = 3000 - 91.139 - 22.785 = 2886.08 s

Answer 2

So the tortoise moves at a steady 0.30 m/s over a 900 m course. That takes him 900m/0.30m/s = 3000 seconds.

If the hare ran without stopping, it would take him 900/7.90 = 113.92 seconds.

The difference should be the time the hare stopped or 3000-113.92 = 2886.08 seconds.

The hare runs at 7.90 m/s sec for 720 m. That takes the hare 720/7.90 = 91.14 seconds. The hare waits for 2886.08 seconds. That means that the hare has spent 91.14+2886.08 = 2977.22 seconds before he starts up again.

Since the tortoise streaks along at 0.30 m/s, he has traveled 0.30 m/s x 2977.22 sec = 893.17 m when the hare starts up. That means he is 900-893.17 = 6.83 m from the finish line when the hare starts up.

Answer 3

So the tortoise moves at a steady 0.300 m/s toward the finish line.

Time taken by tortoise upto finish lane = 0.9*10^3 / 0.3 = 3000 sec

Time taken by hare for 0.72km = 0.72*10^3 / 7.9 = 91.139 s

Time taken by hare from 0.72 to finish line = (0.9-0.72)*10^3 / 7.9 = 22.785 s

a) s = 0.3*22.785 = 6.835 m

b) hare is stationery for time = 3000 - 91.139 - 22.785 = 2886.08 s

Answer 4

So the tortoise moves at a steady 0.300 m/s over a 900 m course. That takes him 900m/0.300m/s = 3000 seconds.

If the hare ran without stopping, it would take him 900/7.90 = 113.9 seconds.

The difference should be the time the hare stopped or 3000 - 113.9 = 2886 seconds. The answer given is either wrong or has serious round-off error.

The hare runs at 7.90 m/s sec for 0.90 km, or 900 m. That takes the hare 900/7.90 = 113.90 seconds. The hare waits for 2886 seconds. That means that the hare has spent 113.90 + 2886 =2999 seconds before he starts up again.

Since the tortoise streaks along at 0.300 m/s, he has traveled 0.30 m/s x 2999 sec = 899 m when the hare starts up. That means he is 900- 899 = 1 m from the finish line when the hare starts up.