Hey Everyone,
This is a deeply bizarre question, and I'd encourage you to be careful where you draw your material from. There are a lot of people writing questions without a strong understanding of what the GMAT does. If you're paraphrasing, this could possibly be made into a real question, but as written, it's just not going to fly. This is for a few reasons:
1) No question in the universe (or none I've seen) is going to mix meters with feet. You might get a question that mixes minutes with hours (Requiring a translation) or miles with feet, but you'll never see one that goes from imperial units to non-imperial units.
2) This question doesn't expressly state where the trains start relative to each other. I suppose we're meant to assume they're nose-to-nose, like so?
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But any real question would be VERY explicit about that.
3) If the answer is going to be approximate, the question would ask for the approximate time.
Okay, now that's that out of the way, Nisagl has it right.
For the sake of fun/reality, I'm going to change 400 meters each into 1200 feet each, to make this more standard (the question would then also say 1 mile = 5280 feet). Once this is done, we can get out our trusty RTD chart (which you should ALWAYS use on rates questions), and solve.
Remember that we can use relative rates here, based on the following rules:
1) If two things are going in opposite directions (either away from or towards each other): add the rates.
2) If two things are going in the same direction: subtract the rates.
In this case, the two trains are going in opposite directions. The only tough thing we need to do is translate our miles per hour into feet per second (assuming that the answer choices were in seconds). 120 miles per hour would be 2 miles per minute, and 2/60 = 1/30 miles per second.
Translated into feet, that's 5280/30 feet per second, which is 176. (You can do this in your head by thinking like so: 3000 = 100 * 30, 6000 = 200 * 30 --> 5280 = 6000 - 720, and 720/30 = 24 --> so 200 - 24 = 176. If that doesn't make sense, you better know how to long divide!).
Rate * Time = Distance
Relative Rate 176 t 1200feet
1200/176 could be ballparked --> 200 goes into 1200 six times, and 150 goes into 1200 eight times, so 7 is probably a safe bet. Again, you could also long divide to get an exact answer.
Hope that helps!
-t
There you go. I answered a different question, but a more realistic one!
-t
Tommy Wallach, Company Expert
ManhattanGMAT
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