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 3.0 minutes. The tortoise wins by a shell (25 cm).(a) How long does the race take? ________s(b) What is the length of the race?________ m

Answer 1

We wioll have the following:

First, we determine the minimum distance traveled.

This velocity is given by the tortoise.

We know that the hare stops for 3 minutes, now we determine the distance that the tortoise traverses in this time:

$d=(0.14m/s)(3min\ast60s/min)\Rightarrow d=25.2m$

And we know that the tortoise won by 25 cm, so the minimum distance traversed will be:

$d_{min}=25.2m+0.25m\Rightarrow d_{min}=25.45m$

So, the minimum distance traversed by both the torotise and the hare is 25.45 m.

a)

Now, we determine the minimum time it took [Using the tortoise's speed], that is:

$\begin{gathered} t=\frac{(25.45m)(1s)}{0.14m}\Rightarrow t=\frac{2545}{14}s \\ \\ \Rightarrow t=181.7857143...s\Rightarrow t\approx181.79s \end{gathered}$

So, it took as a minimum 181.79 s.

b)

The lenght of the total race as a minimum we determined was 25.45 m.