A train leaves a station at 10:00 AM and travels at 60 miles per hour. Another train leaves the same station at 11:00 AM and travels at 75 miles per hour in the same direction. At what time will the second train overtake the first train? SOLUTION

 

In the first hour, the first train travels 60 miles. The second train starts at 11:00 AM and travels at a speed of 75 miles per hour. The second train gains 15 miles per hour on the first train. The second train will overtake the first train at 12:30 PM.

Here's the solution in mathematical form:

Let x be the time in hours it takes the second train to overtake the first train. The first train travels 60x miles in x hours. The second train travels 75(x-1) miles in x-1 hours. Since the two trains travel the same distance, we have the following equation: 60x = 75(x-1) 60x = 75x - 75 15x = 75 x = 5 The second train will overtake the first train at 12:30 PM.