Writing in the Opposite Direction.

Algebra Level 1

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 an hour; and the second starts with the last line then writes line 534 and so on, backward proceeding at the rate of 50 lines an hour. At what line will they meet?

254 357 314 287

Saurav Sah by Saurav Sah , 20, India

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3 solutions

Emmanuel David
Apr 29, 2014

I did a graph

Within 3.5 hours the first boy is on 350 the second is on 360

since the first one had higher rate, I picked 357

3 Helpful 0 Interesting 0 Brilliant 0 Confused
Neil Delos Reyes
Apr 28, 2014

The easiest way to solve the problem is by looking in the interesting fact that the rate of writing backward is half of the rate of writing forward. We know that at a certain time, the one will finish up twice the lines that one had. And for them to meet in one line, the boy writing forward will finish 2/3 of the total lines while the other will finish 1/3 of the total lines. So.. (2/3)*535 = 356.67 and the closest answer in the choices is 357.

3 Helpful 0 Interesting 0 Brilliant 0 Confused
Mayank Holmes
May 26, 2014

since the guy proceeding from the last line writes at a speed which is half of the speed at which the first guy writes, it is clear that when the 1st guy writes X lines... the second one writes (X/2) lines.......... X + (X/2) = 535 and you will get X= 356.67 ( i.e. the they meet at the 357th line )

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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