dog >>5 leaps of 5x
cat>>4 leaps of 6x

(5*5) / (4*6)

note: there is reverse correlation in the equality of leaps.

Lets first assume that a dog leap is equivalent to a cat leap. The ratio of the speed of dog to the speed of cat would simply be 5:6 (for a given period, a dog makes 5 leaps and cat makes 6 leaps).

However, the question states that the length of the dog leap is different from that of the cat leap, and they are related by the following:

4*dog_leap = 5*cat_leap

Going back to the initial problem, we need to have the speeds in equivalent terms, either in terms of dog leaps or cat leaps, and we can convert between the two types with the equation above.

Therefore, the ratio of speeds:

5 dog leaps: 6 cat leaps
5*(5/4) cat leaps: 6 cat leaps
25/4 cat leaps: 6 cat leaps
25 cat leaps: 24 cat leaps

25:24

(Note: I've removed the time element here since they are constants and can be cancelled out since we are dealing with ratios)

-BM-

Nice expalnation BM