Bunuel wrote:
City A and City B are 140 miles apart. Train C departs City A, heading towards City B, at 4:00 and travels at 40 miles per hour. Train D departs City B, heading towards City A, at 4:30 and travels at 20 miles per hour. The trains travel on parallel tracks. At what time do the two trains meet?
A. 5:00
B. 5:30
C. 6:00
D. 6:30
E. 7:00
Kudos for a correct solution.
MANHATTAN GMAT OFFICIAL SOLUTION:Here’s what we need to do to solve the problem.
* First, we must get the trains to
leave at the same time. Train D leaves 30 minutes after train C, so we must find out how far train C has traveled in that first 30 minutes. Remembering that distance equals rate x time, we know that distance = 40 x .5 (note that 30 minutes needs to be expressed in hours.) This tells us that, at 4:30, train C has traveled 20 miles. Thus, our trains are now 120 miles apart.
* At this point all we need to do is
add our rates together, to get the rate at which the trains are traveling towards one another. This gives us 40 + 20 = 60 miles per hour.
* Plug into our three part formula of
D = R x T: 120 = 60 x T, therefore T = 2 hours.
* If we started at 4:30 and traveled for two hours, it is now
6:30, which is the correct answer to this question.
The strategy we just employed will also work on problems in which the trains are traveling away from each other. On test day, rather than feel yourself getting anxious when you see a question that sounds similar to the “Two trains…” scenario, just take a deep breath, envision the scenario, and take it step by step.