Trains A and B start simultaneously from stations 300 miles apart, and travel the same route toward each other...

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Wed Mar 04, 2020 3:16 am

Manhattan Prep

Trains A and B start simultaneously from stations 300 miles apart, and travel the same route toward each other on adjacent parallel tracks. If Train A and Train B travel at a constant rate of 50 miles per hour and 40 miles per hour, respectively, how many miles will Train A have traveled when the trains pass each other, to the nearest mile?

A. 112
B. 133
C. 150
D. 167
E. 188

OA D

I like providing examples that don't involve a lot of equations, since many people struggle in this area.

This is a good problem to back solve using answers. Looking at the list, C 150 looks like the easiest to start with. Also, depending on whether your answer to C is too much or too little, it can eliminate the other choices.

If A has travelled 150mi, this means the trains have travelled for 3hrs. Therefore, B has travelled 120mi. This means they have not passed each other and are still 30mi apart. Eliminate A,B,C

Since they are 30mi apart at this point, it is impossible for A to travel another 38mi to get to 188 and not have passed B already(even if B broke down and didn't move past 120). Therefore eliminate E.

Answer D.