Question

A train leaves Miami at 3:00pm. A second train leaves the same city in the same direction at 5:00pm. The second train travels 50mph faster than the first. If the second train overtakes the first at 7:00pm, what is the speed of each of the two trains.

Answer 1

Let the speed of the first train be v mph. Then the speed of the second train is:
(v + 50) mph.
Distance traveled by the first train from 3pm to 7pm = 4v miles.
The second train travels 4v miles in 2 hours (from 5pm to 7pm). Therefore the speed of the second train = (4v)/2 = 2v.
However the speed of the second train is also given by (v + 50) mph.
v + 50 = 2v
v = 50.
The speed of the first train is 50 mph and the speed of the second train is 100 mph.