trains A and B are traveling in the same direction on paraleel tracks. Train A is traveling at 80 miles per hour and train B is traveling at 88 miles per hour. Train a passes a station at 5:10 P.M. If train B passes the same station at 5:40 P.M., at what time will train B catch up to train A?

Question

trains A and B are traveling in the same direction on paraleel tracks.  Train A is traveling at 80 miles per hour and train B is traveling at 88 miles per hour.  Train a passes a station at 5:10 P.M. If train B passes the same station at 5:40 P.M., at what time will train B catch up to train A?

Steve · Answer

Consider t=0 when train A passes the station. After that, at some time t, the trains will be at the same distance. B travels 0.5 hour less than A.

88(t-.5) = 80t
88t - 44 = 80t
8t = 44
t = 5.5

So, 5.5 hours after 5:10, the trains will have gone the same distance (440 miles) from the station.

That is, at 10:40, B passes A.