rkatl wrote:
Laura 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 respective rates?
A. 1/(3x)
B. 3x/(x-3)
C. (x – 3)/(3x)
D. x/(x-3)
E. (x-3)/x
The Question is a good candidate for plugin...Here is how I would approach
Let us assume value of x for laura to be 12 so we have that laura does 1/12th of room in 20 minutes or to paint one complete laura takes 240 minutes
Let Joseph take y minutes to paint 1 room so we have
Also given that
1/240 +1/y = 1/60 ----> Solve for y and we get y =240/3 or 80 minutes.
(Here we should choose the value of x in such a way that 1/y = \((1/60- 1/x)\geq{0}\) so that y is not negative.
So Joseph paints 1 room in 80 minutes so in 20 minutes, he will paint 1/4th of the room.
Plug in value of x in the above options and we get answer C.
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