## Task 1 - 300731

In a textbook from the year 1525, the following problem is stated in essence:

A dog is hunting a fox. In the time it takes the fox to make 9 jumps, the dog makes 6 jumps, but with 3 jumps, the dog covers the same distance as the fox does with 7 jumps.

How many of its jumps does the dog need to catch up to the fox, if the fox has a 60 fox jumps head start at the beginning?

Note: It is assumed that the dog follows the trail of the fox and that both begin their first jump simultaneously.
In order for the fox to cover the same distance as the dog in the time it takes the dog to make $6=2 \cdot 3$ jumps, the fox would need to make $2 \cdot 7=14$ jumps. However, since the fox only makes 9 jumps in this time, his lead decreases by 5 fox jumps each time.

Since $60: 5=12$, it follows that the lead is exhausted exactly when this happens 12 times, which is after $12 \cdot 6=72$ jumps of the dog.