Question

A cat and a dog have a race. The cat’s strides are 30% shorter than the dog’s but it makes 30% more strides than the dog. Which of them will win the race?

Answer 1

Let
`x` be the length of a cat's stride, and
`y` their stride per time unit ratio.

So, in a time unit, the cat will cover a distance of
`xy`

Dogs strides are 30% longer, do a dog's stride is

`(130)/(100)x = (13x)/(10)`

But its stride per time unit is 30% less:

`(70)/(100)y = (7y)/(10)`

So, in a unit of time, the dog will cover a distance of

`(13x)/(10)(7y)/(10) = (91)/(100)xy`

So, in the same amount of time, the dog covers 91% of the distance of the cat.

Answer 2

Assuming the strides take the same amount of time, the dog wins.

1.30 · 0.70 = 0.91