SOLUTION: If Sally can paint a house in 4 hours and John can paint the house in 6 hours. How long will it take them to paint the house together?

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Question 5093: If Sally can paint a house in 4 hours and John can paint the house in 6 hours. How long will it take them to paint the house together?

Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
If Sally can paint the house in 4 hours, then the part she can do in 1 hour is 1%2F4.

If John can paint the house in 6 hours, then the part he can do in 1 hour is 1%2F6.
Let x = the number of hours it takes them to paint the house together.
If together they can paint the house in "x" hours, then in 1 hour they can paint 1%2Fx of the house.

The equation is "The part Sally can paint in 1 hour + the part that John can paint in 1 hour equals the part they can paint together in 1 hour."
1%2F4+%2B+1%2F6+=+1%2Fx

Multiply both sides of the equation by the least common denominator which is 12x.
%2812x%29%2A%281%2F4%29+%2B+%2812x%29%2A%281%2F6+%29=+%2812x%29%2A%281%2Fx%29+
3x+%2B+2x+=+12
5x+=+12
x=+12%2F5 hours or 2.4 hours.

R^2 at SCC