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?

Question 469791: 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 bucky(2189) (Show Source): You can put this solution on YOUR website!
Since Sally can paint a house in 4 hours, in an hour she completes 1/4 of the house. And since John can paint the same house in 6 hours, in an hour he completes 1/6 of the house. Therefore, in one hour the sum of their combined efforts is:
.

.
of the job.
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Add these two fractions by converting them to the common denominator of 12 to get:
.

.
So in each hour they complete five twelfths of the one job.
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The question, therefore, is how many hours (call them t for time) does it take for them to complete the entire one job (that is 12 twelfths of the job). Set up the following equation:
.

.
Solve this equation by first multiplying both sides of the equation by 12 to eliminate the denominator of 12 and get:
.

.
Solve this equation by dividing both sides by 5:
.

.
and divide 12 by 5 to get the answer:
.

.
So it takes 2.4 hours for them working together to paint the house. (And since there are 60 minutes in an hour, the 0.4 of an hour is minutes.) Therefore, working together they will complete the job in 2 hours and 24 minutes.
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Hope this helps you to understand the problem better.
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