Distance Problem

Question

Hello,

Trying to confirm if 26 meters is the correct answer for the problem below:

A fox notices a rabbit that is 30 meters away. The fox's leap is 2 meters whereas the rabbit's leap is 1 meter. If the fox can take 3 leaps in the time that the rabbit can take 2 leaps, what distance will the fox have to cover in order to catch the rabbit?

Thank you.

Answer 1

Let x = the distance the the animals are from the fox's starting point at the time when the fox overtakes the fox.

Assuming the leaps of each animal take the same amount of time, then the fox travels 2 meters/leap and the rabbit 1 meter/leap.

For the fox x = 2L.

For the rabbit x = 30 + L (rabbit had a 30 meter head start).

At the time the fox overtakes the rabbit these values are equal.

2L = 30 + L

L = 30

That is, it takes 30 leaps for the fox to overtake the rabbit.

After 30 leaps the fox will be 60 meters from its starting point.

After 30 leaps the rabbit will be 60 meters from the fox's starting point. Poor rabbit.

Visit this graph and click on the play button on row 4 to see the fox overtake the rabbit.

desmos.com/calculator/2h5cfwob5z