A train leaves San Diego at 1:00 pm. A second train leaves the same city in the same direction at 3:00 pm. The second train travels 30 mph faster then the first. If the second train overtakes the first at 6:00 pm, what is the the speed of each of the two trains?

The speed of the first train is 45 mph and the speed of the second train is 75 mph

Step-by-step explanation:

Let x represent the speed of the first train in mph. Since the second train, is 30 mph faster then the first, therefore the speed of the second train is (x + 30).

The first train leaves at 1:00 pm, therefore at 6:00 pm, the time taken is 5 hours. Therefore the distance covered by the first train at 6:00 pm = x mph * 5 hours = 5x miles

The second train leaves at 3:00 pm, therefore at 6:00 pm, the time taken is 3 hours. Therefore the distance covered by the second train at 6:00 pm = (x + 30) mph * 3 hours = (3x + 90) miles

Since the second train overtakes the first at 6:00 pm, hence:

3x + 90 = 5x

2x = 90

x = 45

Therefore the speed of the first train is 45 mph and the speed of the second train is 75 mph (45 mph + 30 mph).