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

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

by AAPL » Wed Mar 04, 2020 3:16 am

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

by jbryant62 » Wed Mar 04, 2020 9:48 am
AAPL wrote: ↑
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.
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Re: Trains A and B start simultaneously from stations 300 miles apart, and travel the same route toward each other...

by Scott@TargetTestPrep » Fri Mar 06, 2020 7:43 am
AAPL wrote: ↑
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
We can let time of trains A and B = t and create the following equation:

50t + 40t = 300

90t = 300

t = 300/90 = 10/3 hours

So train A will have traveled 50 x 10/3= 500/3 = 166 2/3 miles by the time they passed, which is closest to the answer of 167.

Answer: D

Scott Woodbury-Stewart
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