A hare and a tortoise compete in a race over a straight course 0.75 km long. The

Question

A hare and a tortoise compete in a race over a straight course 0.75 km long. The tortoise crawls at a speed of 0.110 m/s toward the finish line. The hare runs at a speed of 7.00 m/s toward the finish line for 0.600 km and then stops to tease 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 7.00 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? m (b) For how long in time was the hare stationary? s

Explanation / Answer

So the tortoise moves at a steady 0.11 m/s over a 0.750 km course. That takes him 750m/0,11m/s = 6818.1818 seconds.

If the hare ran without stopping, it would take him 750/7.00 = 107.1428 seconds.

b) The difference should be the time the hare stopped or 6818.1818 - 107.1428 = 6711.039 seconds.
The hare runs at 7.00 m/s sec for 0.60 km, or 600 m. That takes the hare 600/7.00 = 85.714 seconds.

The hare waits for 6711.039 seconds. That means that the hare has spent 85.714 + 6711.039 = 6796.753 seconds before he starts up again.

a) Since the tortoise streaks along at 0.11 m/s, he has traveled 0.11 m/s x 6796.753 sec = 747.64286 m when the hare starts up. That means he is 750 - 747.64286 = 2.36 m from the finish line when the hare starts up

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