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Writing Speed(plz explain)

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by akpareek » Fri Apr 09, 2010 8:06 am
Two boys begin together to write out a booklet containing 535 lines. the first boy starts with the first line, writing at the rate of 100 lines per hour; and the second starts with the last line then writes line 534 and so on, backward proceeding at the rate of 50 lines per hour. At what line will they meet.

A. 356
B. 357
C. 277
D. 267
E. 257
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by student22 » Fri Apr 09, 2010 9:35 am
This is a variation of the two airplanes flying at each other problem.

Here's how to solve it, add the two rates together, 100 + 50 = 150.

Now use the rate formula of r * t = d

So set the rate equal the total amount (or distance): 150t = 535 ---> t = 3.566667.

That means that they will meet in 3.5666667 hours, so simply plug that time back into one of the two rates to see what page they will meet at:

100 (3.56) = 356.

or

100 (3.57) = 357.

I'm really not sure how it wants you to round this problem. I've never seen an official GMAT problem this ambiguous. But it's either A or B. Similar problems that I've seen always divide cleanly or at least have terminating decimals (i.e. 3.25)
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by ymach3 » Sat Apr 10, 2010 12:01 am
100 t =535

50t=535-x

When solved, we get x =535-267.5=267 lines.

Option-D

Did i mess it up somewhere ??
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by this_time_i_will » Sat Apr 10, 2010 12:45 am
akpareek wrote:Two boys begin together to write out a booklet containing 535 lines. the first boy starts with the first line, writing at the rate of 100 lines per hour; and the second starts with the last line then writes line 534 and so on, backward proceeding at the rate of 50 lines per hour. At what line will they meet.

A. 356
B. 357
C. 277
D. 267
E. 257
The easiest way to solve this and other similar questions is to use relative speed concept of Time & Distance type problems.
Let the distance = 535 lines.
relative speed = 100+50 = 150 lph.
so both meet at = 535/150 = 3.566 hrs

So, in 3.566 hrs, first boy would have reached at line number = 3.566*100 = 356.6 .
= this means the first boy would be writing 357th line.
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by pops » Sat Apr 10, 2010 12:49 am
ymach3 wrote:100 t =535

50t=535-x

When solved, we get x =535-267.5=267 lines.

Option-D

Did i mess it up somewhere ??
aye, 100t = x (and not 535, accroding to you A is writing all the 535 lines)
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by akpareek » Sat Apr 10, 2010 10:06 am
Thanks Guys !!!!!!!
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