Question

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 race track is a distance, d. The race is considered over when the tortoise crosses the finish line.

Using the symbols of the problem, write an equation for the amount of time that the hare ran,
`\Delta t_H`.

Answer 1

`t_(H) = t_(T) - 60`

Step-by-step explanation:

Thinking process:

Let:

distance = speed × time

for the hare:

`d_(H) = s_(H) t_(H)`

for the tortoise:

`d_(T) = s_(T) t_(T)`

Let the length of the shell be s. Then the two are related. So:

`d_(H) = d_(T) - s`

Let's say the hare ran at x times the speed of the tortoise:

`s_(H) = xs_(T)`

So, the equation still holds :
`t_(H) = t_(T) - 60`