Rates In Terms of Variable

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avada: Senior | Next Rank: 100 Posts; Posts: 38; Joined: Fri Aug 17, 2012 11:28 am; Thanked: 2 times

Rates In Terms of Variable

by avada » Sat Sep 01, 2012 9:46 am

I am struggling a little bit with rates but I am really struggling with working on problems with answers in terms of variables. My study books recommend I use made up numbers. What strategy do you use?

Question is from MCAT online
Machine A can complete a certain job in x hours. Machine B can complete the same job in y hours. If A and B work together at their respective rates to complete the job, which of the following represents the fraction of the job that B will not have to complete?
(X-Y)/(X+Y)
X/(Y-X)
(X+Y)/XY
Y/(X-Y)
Y/(X+Y)

Quote

Source: Beat The GMAT — Problem Solving | Sat Sep 01, 2012 9:46 am

adthedaddy: Master | Next Rank: 500 Posts; Posts: 167; Joined: Fri Mar 09, 2012 8:35 pm; Thanked: 39 times; Followed by:3 members

by adthedaddy » Sat Sep 01, 2012 10:06 am

Combined rate = 1/x + 1/y = (x+y)/xy

Combined work done = xy/(x+y)

Work done by A = (1/x)*(xy/x+y) = y/(x+y)
Work done by B = (1/y)*(xy/x+y) = x/(x+y)

Now, B will not have to complete the work which is already done by A which is y/(x+y)

[spoiler]Ans: y/(x+y)[/spoiler]

Last edited by adthedaddy on Sat Sep 01, 2012 10:11 am, edited 1 time in total.

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