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Whole Train Question

by Bunmiafolabi » Tue Jan 22, 2013 8:03 am
Please can anyone explain the solution to this question - How long does it take the whole of a train that is 1mile long to pass through a 5 mile tunnel, travelling at 60mph?

Answers are 7, 4, 5, 6 and 10 minutes.

thanks.
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by GMATGuruNY » Tue Jan 22, 2013 9:17 am
Bunmiafolabi wrote:Please can anyone explain the solution to this question - How long does it take the whole of a train that is 1mile long to pass through a 5 mile tunnel, travelling at 60mph?

Answers are 7, 4, 5, 6 and 10 minutes.

thanks.
<---TRAIN = 1 mile---><----------TUNNEL = 5 miles---------->

The back of the train must travel 1+5 = 6 miles to reach the end of the tunnel.
Time for the back of the train to travel 6 miles = d/r = 6/60 = 1/10 of an hour = 6 minutes.

The correct answer is D.
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by Tommy Wallach » Tue Jan 22, 2013 9:41 am
Hey Bunmiafolabi,

So the thing to remember about this question is that when we calculate rates, we're usually talking about the FRONT of a given vehicle. In this case, when the front of the train has gone from the entrance of the tunnel to the end of the tunnel, there's still a mile of train left. In pictures:

TUUUUUUUUUUUUUUNNNNNNNNNNNNNNEEEEEEEEELLLLLLLLL [1 mile long]
[5 miles long] TTTRRRAAAIIINNN

We aren't happy until this moment has been reached, and the last part of the train is out. So if the train started at the mouth of the tunnel, we aren't happy until the front of the train has gone 6 miles (all through the tunnel, and a mile farther, as in the picture). How long does it take something to go 6 miles at 60mph? 6 minutes!

Hope that helps!

-t
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by buzzdeepak » Tue Jan 22, 2013 11:12 am
I quickly drew a picture to solve this:

|-| _ _ _ _ _

(|-| is the train and the 5 underscores represent 5 miles in the tunnel - Easier to draw on paper than on this screen)

60 mph = 1 m / min (since answers are in mins)

Tunnel is 5 miles long, so when the front of the train reaches the end of tunnel, it would have covered 5 miles, so it requires 5 mins.

Now the train is 1 mile long and for the last part of the train to be out, it needs to go a mile further, i.e., 1 min.

Hence total time = [spoiler]5+1 = 6 mins[/spoiler]

Hope this helps..
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by Tommy Wallach » Tue Jan 22, 2013 4:38 pm
Hey Buzzdeep/Bunmi,

Indeed, this forum did not translate my own attempt at a picture very well at all! But yes, drawing this can be very helpful.

Another way to think of it is that the back of the train has to get from where it starts (a mile away from the tunnel entrance) to the end of the tunnel. That's six miles right there.

-t
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by Bunmiafolabi » Wed Jan 23, 2013 8:31 am
Thanks everyone. Can you believe I had the reasoning right but for some strange reason my brain kept doing 60/6 instead of 6/60 and thus I couldn't figure out why I was getting the wrong answer! I feel like beating myself. Thanks Again. Really need to be more careful.
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