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Question 266020: Two brothers are digging a drainage ditch for a french drain around their home. The ditch is to be 2 feet deep, 1 foot wide, and 40 feet long. The older brother can dig the ditch in 14 hours. The younger brother can dig the ditch in 17 hours. How long will the two brothers working together take to dig the ditch? (Round your answer to the nearest tenth.)
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website!
Let x=amount of time it takes the two brothers working together
Then the two bros dig at the rate of 1/x ditch per hour
Older bro digs at the rate of 1/14 ditch per hour
The younger bro digs at the rate of 1/17 ditch per hour
The two bros dig at he rate of 1/14 + 1/17 ditch per hour
So, our equation to solve is:
1/14 + 1/17=1/x Multiply each term by 14*17*x
17x+14x=238
31x=238
x=238/31
x=7.677 hours=7.7 hours---answer
CK
In 238/31 hours, older bro digs (1/14)*(238/31) =17/31 of the ditch
In 238/31 hours the younger bro digs (1/17)*(238/31) =14/31 of the ditch
17/31 + 14/31=1 (1 ditch, that is)
1=1
Hope this helps-ptaylor
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