I will refer to the cheetah as C, and the prey as P.
Okay, so the distance travelled by C at any point in time, t, is given by:
(This is found using distance = speed * time if that wasn't self-evident.)
Similarly, the distance travelled by P is given by:
Initially, the prey is 300 feet ahead of the cheetah, so to catch up, the cheetah needs to travel 300 metres more that the prey. That is:
Plugging in the values from our previous equations gives
90t = 70t + 300
=> 70t = 300
=> t = 15
So the cheetah cathes its prey at 15s.
We can check this by substituting t = 15 into our original equations:
= 90 * 15 = 1350 feet
= 70 * 15 = 1050 feet
This is correct as the cheetah has travelled 300 feet more than the prey, accounting for the initial seperation distance.