John is driving north at 60 mph. Yes leaves the same place two hours later, and drives along John's path at 75 mph. How long does it take Ted to catch up to John? How long has Ted been driving?

To solve this problem, we want to know in what hour the distances traveled by both are equal.

We know that Ted is traveling at 75 mph, and he must drive the hours to get to John. So, the distance that Ted must travel to get to John is

d = 75t

On the other hand, in (2 + t) hours John will have traveled a distance:

d = (2 + t) * 60

To find the value of t (the time Ted reaches John) we equate both equations:

(2 + t) * 60 = 75t

120 + 60t = 75t

120 = 15t

t = 120/15

t = 8h.

Finally Ted has driven 8 hours to get to John.