Question and Formula Setup:

If train A leaves the station going 50 miles an hour, and train B leaves the station one hour later going 70 miles an hour, how many miles will it take for train B to catch up with train A?

If train A is going 50 miles/hour, then the amount of distance it can

go in a certain time (call it t) is:

   50 miles/hour * t hours = 50t miles

The second train starts out 1 hour later, so for it the time it is

travelling is t-1. That means that train B (going 70 miles per hour)

can go this distance in t-1 hours:

   70 miles/hour * (t-1) hours = 70(t-1) miles

The question says that train B catches up with train A (which mean

that they go the same distance), so that means:

   50t = 70(t-1)

Solve for t to find the number of hours the trains were travelling.

Solution:

   50t = 70t - 70

   70 = 70t - 50t

   70 = 20t

   70/20 = t

   3.5 = t

   t = 3.5 miles