Question

a dog starts chasing a cat when they are 12 meters. for every 7 meters that the dog runs, the cat runs 4 meters. how far does the dog have to run to catch up with the cat?

Answer 1

Let the distance run by the dog be 7x m
let the distance run by the cat be 4x m

so 7x = 4x + 12
3x = 12
x = 4

So the dog has to run 7(4) or 28 m to catch the cat.

check:
In the same time that the dog ran 28 m , the cat ran
16 m
but the cat had a 12 m head-start , giving us also 16+12 or 28 m