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

Answer: the speed of the first train is 50 mph.

The speed of the second train is 100 mph.

Step-by-step explanation:

Let x represent the speed of the first train. The second train travels 50mph faster than the first. It means that the speed of the second train is (x + 50) mph.

Distance = speed * time

If the second train overtakes the first at 7:00 PM, it means that both trains covered the same distance by 7:00 PM. The first train left Miami at 3:00PM. Time spent by the first train is 7 - 3 = 4 hours

Distance covered by the first train in 4 hours is 4x

The second train left at 5:00 PM. Time spent by the second train is 7 - 5 = 2 hours

Distance covered by the second train in 2 hours is 2 (x + 50)

Therefore,

4x = 2 (x + 50)

4x = 2x + 100

4x - 2x = 100

2x = 100

x = 100/2

x = 50 mph

The speed of the second train is

x + 50 = 50 + 50 = 100 mph