# A hare and a tortoise compete in a race Question? Distance and Time?

Hi, I'm new to the physics realm and have been out of school for quite some time, and am having difficulties on what most would consider trivial. If anyone has any insight on the following question, as to how I would proceed with it and which equations to use, it would be greatly appreciated. I'm thinking there's a few steps I need to do to get to the solution. Unfortunately I'm rusty on calculus as well, so if there is perhaps another way to solve it.

"A hare and a tortoise compete in a race over a straight course 1.75 km long. The tortoise crawls at a speed of 0.100 m/s toward the finish line. The hare runs at a speed of 7.35 m/s toward the finish line for 1.400 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 7.35 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?

Simon Bridge
Homework Helper
It's all in the setup.

The finish line is a big distance D away.
The tortoise runs at speed u all the way to the finish.
The time it takes the tortoise to finish the race is... T=? (when you see a question mark - you do it.)

The Hare runs at speed v > u
BUT, the hare stops at t=T1, has a rest, and starts again at t=T2.
T1 is the time it takes the hare to travel a smaller distance d ... so you can write that T1=???

Next is the hard part - T2 is special ... it is the last instant the hare can start running again to finish the race at the same time as the tortoise.

What is the distance remaining in the race?
How long does it take the hare to run that far?
So what time is t=T2?

Now you should be able to work out the questions.