Question 266020

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