You are in the center of a circular lake The animal likes to

You are in the center of a circular lake. The animal likes to be close to water, so it only moves around the lake. Its moving speed is 4x greater than your swimming speed. The goat can change its direction of movement (i.e. run around the lake in the opposite direction) any time it wants and as many times as it wants. Can you escape the lake without running into the goat? If yes, explain how. If no, explain why.

Solution

The swimmer needs to cover the distance of r to reach the end of the lake

Let the speed of swimmer be x

speed of goat >= 4x

Since the goat is moving on the circumference of the circle, the distance covered in each round is equal to 2 * pi * r

Time taken to cover the distance r/x if going straight, in that much time it can cover a distance of greater than equal to 4r

Hence the distance is equal to 2 * pi * r = 2 * 3.14 * r = 6.28r

But since the goat can reverse it\'s direction, it will be maximum of pi * r distance from any point which is equal to 3.14r

Hence the lake cannot be escaped without running into the goat