Question

A speedy tortoise can run with a speed of bsmiddle" class="latex-formula"> 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

Answer:

$t_{H} = t_{T} - 60$

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 : $t_{H} = t_{T} - 60$