Problem 23.

A tortoise and a hare are in a road race to defend the honor of their breed. The tortoise crawls the entire 1000 meters at a speed of 0.2 m/s. The rabbit runs the first 200 meters at 2 m/s, stops to take a nap for 1.3 hours, and awakens to finish the last 800 meters with an average speed of 3 m/s. Who wins the race and by how much time?

Solution:

At first let us calculate the traveled time of tortoise. We know the speed and the distance, so we can easily find the time:

Now let us calculate the traveled time of rabbit. The traveled time consists of three parts:

1. He runs the first 200 m at 2 m/s. The time of this motion is

2. Then he take a nap for 1.3 hours:

3. Then he run the last 800 m with speed 3 m/s. The time of this motion is

Then the total traveled time is

Since then tortoise wins the race by 47 s.