Question

A tortoise can run with a speed of 0.14 m/s, and a hare can run 20 times as fast. In a race, they both start at the same time, but the hare stops to rest for 1.0 minutes. The tortoise wins by a shell (30 cm). (a) how long does the race take? S (b) what is the length of the race?

Answer 1

speed of tortoise is given as v1 = 0.14 m/s

speed of hare is given as v2 = 20*0.14 = 2.8 m/s

now let say the total length of the path is "d"

so the total time taken by the tortoise to cover this

$t = \frac{d}{0.14}$

now given that hare took rest for 1 min

so total time of run for hare is (t - 60)s

so the distance that hare covered is given by

$d - 0.30 = 2.8 * (t - 60)$

now by above two equations

$d - 0.30 = 2.8 * \frac{d}{0.14} - 168$

$168 - 0.30 = (20 - 1)d$

$d = 8.82 m$

and the time t is given by

$t = \frac{8.82}{0.14}$

$t = 63 s$

so part a)

t = 63 s

part b)

d = 8.82 m