Problem 62.

A tortoise can run with a speed of 10.0 cm/s, and a hare can run exactly 10 times as fast. In a race, they both start at the same time, but the hare stops to rest for 3.00 min. The tortoise wins by 10 cm.

(a) How long does the race take?

(b) What is the length of the race?

Solution:

(a) If L is the length of the race then the tortoise run this race the time:

When the tortoise crosses the finish line the hare is 20 cm=0.2 m behind tortoise. It means that during time it traveled the distance L-0.2. Since he stopped for rest for 3 minutes =3*60 s=180 s and his speed is , then we can write the equation:

Taking into account the first equation we have:

Then

(b) Then we can find the length of the race: