SOLUTION: sally can paint a house in 4 hours john can paint the same house in 6 hours how long would it take both to paint the house together?

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Question 643992: sally can paint a house in 4 hours
john can paint the same house in 6 hours
how long would it take both to paint the house together?
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
If Sally can paint a house in 4 hours, then she can paint 1%2F4+of a house in 1 hour.
If John can paint a house in 6 hours, then he can paint 1%2F6 of a house in 1 hour.
Let x be the number of hours it would take them to paint the house.
Working together, they can paint 1%2Fx of the house in 1 hour, so
1%2F4+%2B+1%2F6+=+1%2Fx
Multiply by LCD, so 12%281%2F4+%2B+1%2F6%29+=12%281%2Fx%29
12%281%2F4%29+%2B+12%281%2F6%29+=12%2Fx
cross%2812%293%281%2Fcross%284%291%29+%2B+cross%2812%292%281%2Fcross%286%291%29+=12%2Fx
3%2B2=12%2Fx
5=12%2Fx
5x=12
x=12%2F5
x=2.4 hours. Also, 0.4=40 % of 60 minutes is 24 minutes.
Final answer = 2 hours and 24 minutes.