20 minutes is 1/3 of an hour. In an hour, Laura would paint
3 * 1/x = 3/x;
Joseph, then, would have painted the rest:
1 - 3/x, or (x-3)/x.
So in 20 minutes Joe would do
(x-3)/3x.

Good one haas and brain... i was stuck on how to start this one out but you guys are right on the nose..


C.

3(1/x) +3(1/y) = 1

(1/y) = 1/3 - 1/x

1/y = (x-3)/3x

3-C

Laura can paint 1/x of room in 20 mins
Hence in 1 min she can paint 1/20x of room

Let Joseph paints 1/J of the room in 1 min

Hence
1/20x + 1/J = 1/60
1/J = x-3/60x
Hence J= 60x/x-3

Therefore in 60x/x-3 mins joseph paints 1 room
in 20 mins he can paint = 20 * (x-3) / 60x = (x-3)/3x of the room

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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“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

Options with variables are often done by plugging in numbers.
Both working together can paint the room in 1 hr so if their individual rates were equal, each would take 2 hours alone.
2 hours is 120 mins so in 20 mins each would complete 120/20 = 1/6th of the room alone.
So if x = 6 (Laura completes 1/6th of the room in 20 mins), the correct option will give 1/6. (Joseph will also paint 1/6th of the room if their rates are same)
If you put x = 6 in the options, only option (C) will give 1/6

Answer (C)
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Together they paint 1 room in 60 min. So in 20 min they paint (1/3) room. Out of this Laura painted (1/x) room, so Joseph must have painted (1/3) - (1/x) room => (x – 3)/(3x) room