Two trains continuously travel between Washington DC

Vincen wrote: ↑

Wed Sep 20, 2017 8:06 am

Two trains continuously travel between Washington DC and Baltimore, which is 120 miles away. They start simultaneously, train A at Washington and train B at Baltimore, and run at 30 and 90 mph respectively. The station turnaround times are negligible. What is the distance between the point where the trains meet for the first time and the point where they meet for the second time?

A) 0
B) 30 miles
C) 60 miles
D) 90 miles
E) 120 miles

B is the OA.

Can anybody do a graph where I can see the two points where the meet each other? It would be helpful.

The point where the two trains meet for the first time is the point when they together travel the distance between Washington DC and Baltimore once. So let t be the time when they together travel the distance between Washington DC and Baltimore once and we can create the equation:

30t + 90t = 120

120t = 120

t = 1

Therefore, the meeting point for the first time is 30 miles from Washington DC (or 90 miles from Baltimore).

Similarly, the point where the two trains meet for the second time is the point when they together travel the distance between Washington DC and Baltimore twice. So let m be the time when they together travel the distance between Washington DC and Baltimore twice and we can create the equation:

30t + 90t = 240

120t = 240

t = 2

Therefore, the meeting point for the second time is 60 miles from Washington DC (or 60 miles from Baltimore).

Therefore, the distance between the two meeting points is 60 - 30 = 30 (or 90 - 60 = 30) miles.

Answer: B