The turtle crawls along the plane at a constant speed, changing direction 90 degrees every 15 minutes.

The turtle crawls along the plane at a constant speed, changing direction 90 degrees every 15 minutes. Prove that she can return to the “start” point only after a whole number of hours after the start of the movement

First, let’s clarify that 90 degrees is a right angle. It is logical that there can be only 4 right angles. Accordingly, in this case the turtle can only crawl on a square plane.

Let’s calculate how many times the turtle needs to change direction to return to the starting point:

360 degrees / 90 degrees = 4 times.

Therefore, let’s calculate how long it will take for the turtle to pass the square plane and return to the starting point:

4 times * 15 minutes = 60 minutes = 1 hour.

Answer: Indeed, the turtle will be able to return to the starting point only after a whole number of hours, namely after 1 hour.