Question 18846: If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together?
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! You can start by finding the rate (how much per hour) at which Sally and John can paint.
If Sally can paint the entire house in 4 hours, then she can paint 1/4 of the house in 1 hour.
If John can paint the entire house in 6 hours, then he can paint 1/6 of the house in 1 hour.
Together, they can paint (1/4 + 1/6 = 3/12 + 2/12 = 5/12) of the house in 1 hour.
You could make a little equation from this, where H = the house:
(5/12)H = 1 hour.
To find 1 H, you would multiply both sides by the multiplicative inverse of 5/12, that's 12/5.
H = 12/5 hours
So, together they can paint the entire house in 12/5 hrs. = 2 2/5 hrs. = 2 hours 24 minutes.
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