SOLUTION: 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? I did not get the answer t

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Question 22995: 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?
I did not get the answer to this problem, so if you could please give me some solutions.

Found 2 solutions by rapaljer, AnlytcPhil:
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 in 1 hour she can paint 1/4 of the house.
If John can paint the house in 6 hours, then in 1 hour he can paint 1/6 of the house.
Let x = number of hours it would take them together to paint the house, then working together, in 1 hour they can paint 1/x of the house.

The equation is this:
1%2F4+%2B+1%2F6+=+1%2Fx

Multiply both sides by the LCD 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 = 2.4 hours

R^2 at SCC

Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!
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? 
I did not get the answer to this problem, so if you could please give me some
solutions.

Let x = the number of hours it will take them painting together

Then their combined rate = (1 house)/(x hours) or 1/x house/hr

>>...Sally can paint a house in 4 hours...<<

Translation:  Sally's rate is (1 house)/(4 hours) or 1/4 house/hr

>>...John can paint the same house in 6 hour...<<

Translation: John's rate is (1 house)/(6 hours) or 1/6 house/ hr

To form the equation:

Sally's rate + John's rate = their combined rate

1/4 + 1/6 = 1/x

Can you solve that?  (Hint: get LCD = 12x and multiply thru)

Answer: 2.4 hours or 2 hours 24 minutes

Edwin
AnlytcPhil@aol.com