mathschallenge.net

Problem

A tortoise and a hare race against each other.

A hare runs at a constant speed of 36 km per hour for exactly ten seconds and waits for the tortoise to catch up.

If the tortoise takes two hours to move 1 km, how long will it take to catch up?

Solution

36 km per hour is equivalent to 0.6 km per minute, or 600 m per minute, which is the same as 10 m per second. Hence the hare has run a distance of 100 m in 10 s.

If the tortoise takes 2 hours = 120 minutes to move 1 km = 1000 m, it will take 12 minutes to move 100 m.

How long would the tortoise take to run 1 mile?
Assuming the hare can maintain its speed, how many miles would the hare have run in the same time?