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A speedy tortoise can run with a speed of [tex]v_T[/tex] and a hare can run with a speed [tex]v_H[/tex]. 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, [tex]\Delta t_H[/tex].

Respuesta :

tatendagota

Answer:

[tex]t_{H} = t_{T} - 60[/tex]

Explanation:

Thinking process:

Let:

distance = speed × time

for the hare:

[tex]d_{H} = s_{H} t_{H}[/tex]

for the tortoise:

[tex]d_{T} = s_{T} t_{T}[/tex]

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

[tex]d_{H} = d_{T} - s[/tex]

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

[tex]s_{H} = xs_{T}[/tex]

So, the equation still holds : [tex]t_{H} = t_{T} - 60[/tex]