Lindsay can paint 1/x of a certain room in 20 minutes. What fraction of the same room can Joseph paint in 20 minutes if the two of them can paint the room in an hour, working together at their respectives rates?
A. 1/3x
B. 3x/(x - 3)
C. (x - 3) / 3x
D. x / (x - 3)
E. (x - 3) / x
Let the room = 20 units.
Let x = 4.
Since Lindsay paints 1/x of the room in 20 minutes -- the equivalent of 1/3 hour -- Lindsay's rate = (1/4) * 20 = 5 units per 1/3 hour = 15 units per hour.
Since Lindsay and Joseph paint the entire room in 1 hour, their combined rate = 20 units per hour.
Thus, Joseph's rate = (combined rate) - (Lindsay's rate) = 20-15 = 5 units per hour.
In 20 minutes -- the equivalent of 1/3 hour -- the amount of work produced by Joseph = r*t = 5 * (1/3) = 5/3 units.
Thus, the fraction painted by Joseph = (5/3)/20 = 1/12. This is the target.
Now plug x=4 into the answers to see which yields the target value of 1/12.
Only C works:
(x-3)/3x = (4-3)/(3*4) = 1/12.
The correct answer is
C.
Last edited by GMATGuruNY on Sun Sep 30, 2018 9:48 am, edited 1 time in total.
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