SOLUTION: Hi. I can across this question in the practice Accuplacer test, and I cannot for the life of me figure out how to work it. 2. If Sally can paint a house in 4 hours, and John can

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Question 233246: Hi. I can across this question in the practice Accuplacer test, and I cannot for the life of me figure out how to work it.
2. 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?
A. 2 hours and 24 minutes
B. 3 hours and 12 minutes
C. 3 hours and 44 minutes
D. 4 hours and 10 minutes
E. 4 hours and 33 minutes
I know that the answer is A, however I do not know how. Your help is greatly appreciated.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
2. 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?
:
Here's an easy method to do these "shared work" problems
:
Let t = time required when they work together
:
Let the completed job = 1; (a painted house in this case)
:
Each person will do a fraction of the work, the two fractions add up to 1
t%2F4 + t%2F6 = 1
multiply equation by 12 to get rid of the denominators, results:
3t + 2t = 12
:
5t = 12
t = 12%2F5
t = 2.4 hrs working together
Convert .4 hrs to min: .4 * 60 = 24 min
t = 2 hr 24 min
:
:
You can prove this to yourself:
2.4%2F4 + 2.4%2F6 =
.6 + .4 = 1
:
Wasn't that pretty easy to understand??