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Rate problem... can you help?

by mjjking » Fri Feb 27, 2009 1:51 am
Jack takes 2 more hours than Tom to type 20 pages. Working together they can do 25 pages in 3 hours. How long will it take Jack to type 40 pages?

(A) 5
(B) 6
(C) 8
(D) 10
(E) 12

I miss something in reaching the answer, I get that their combined rate is 25/3 but then?

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by bluementor » Fri Feb 27, 2009 2:08 am
Working together they can do 25 pages in 3 hours

So, time taken to do 20 pages, while working together is:

(20/25)*3 = 12/5 hrs

To do 20 pages:

Tom alone takes x hours
Jack alone takes x+2 hours
Both together take 12/5 hours

1/x + 1/(x+2) = 1/(12/5)
(x + 2 + x)/(x^2 + 2x) = 5/12
12*(2x + 2) = 5*(x^2 + 2x)
5x^2 - 14 - 24 = 0
(5x + 6)(x - 4)= 0
x = 4 (since time value must be positive).

Jack takes 6 hours to type 20 pages alone.
Therefore, Jack will take 12 hours to type 40 pages alone.

Choose E.

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