A speedy tortoise can run with a speed of v_T and a hare can run with a speed v_H. The hare waits to rest for a time Δt₀ after the race begins and the tortoise starts and then runs as fast as he can, but the tortoise still wins by a shell (length of shell = s). The length of the racetrack is a distance, d. The race is considered over when the tortoise crosses the finish line.

a. Using the symbols of the problem, write an equation for the amount of time that the tortoise ran, Δt_T.

b. Using the symbols of the problem, write an equation for the amount of time that the hare ran, Δt_H.

c. If you only know the speeds of the tortoise and the hare, the rest time and the length of the shell, can you find the length of the racetrack and the times that the animals each ran?

Joe Redish 8/16/15