SOLUTION: if Jane takes 5 hours to paint a house and John takes 6 hours to paint a house. How long will it take them working together?

Question 4327: if Jane takes 5 hours to paint a house and John takes 6 hours to paint a house. How long will it take them working together?
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
If Jane can paint a house in 5 hours, then in 1 hour she can paint of it.
If John can paint the house in 6 hours, then in 1 hour he can paint of the job.
Let x = the time it would take them to paint the house together.
Then in 1 hour, together they could paint 1/x of the house.

So, the equation is then: What Jane can paint in 1 hour, plus what John can paint in 1 hour, equals what they can paint together in 1 hour, or as follows:

This equation can be solved in two ways. For those who do NOT like fractions, you can multiply both sides of the equation by the Least Common Denominator (LCD), which in the case is 30x:

Reduce all the fractions, which eliminates all the denominators:

hours

R^2 at SCC

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