SOLUTION: I need your help!! I can't figure out this word problem!! George can install new wiring for a company in 3 hours. It takes Pete 4 hours to do the same job. How long will it take

Question 62077: I need your help!! I can't figure out this word problem!!
George can install new wiring for a company in 3 hours. It takes Pete 4 hours to do the same job. How long will it take if they work together?
Answer by joyofmath(189) (Show Source): You can put this solution on YOUR website!
George can install new wiring for a company in 3 hours. It takes Pete 4 hours to do the same job. How long will it take if they work together?
First guesstimate at the answer. This will give you a sense of whether you got it right or not once you've solved it. George works faster. With Pete's help the work will get done faster but not twice as fast.
Now, George can do the all of the work, let's call it W, in 3 hours. So, George can do 1/3 W in 1 hour.
Pete can do all of the work in 4 hours. So, Pete can do 1/4 W in 1 hour.
So, in 1 hour George and Pete together can do 1/3W+1/4W = (7/12)W. So,
(7/12)W = 1 hour. Multiply both sides of the equation by 12/7. Then, all of the work can be done by the two together in 12/7 hour, or 1 5/7 hour, or about 1 hour 43 minutes.
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