SOLUTION: Ben finish a job 2 hours longer than Daniel. After Ben had been working for 1 hour Daniel joined him and they completed the remaining portion of the job for 3 hours. How long would

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Ben finish a job 2 hours longer than Daniel. After Ben had been working for 1 hour Daniel joined him and they completed the remaining portion of the job for 3 hours. How long would      Log On


   

Question 1122892: Ben finish a job 2 hours longer than Daniel. After Ben had been working for 1 hour Daniel joined him and they completed the remaining portion of the job for 3 hours. How long would it take Ben to do the job?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Ben finish a job 2 hours longer than Daniel.
After Ben had been working for 1 hour Daniel joined him and they completed the remaining portion of the job for 3 hours.
How long would it take Ben to do the job?
:
d = time required by Daniel to complete the job
"Ben finish a job 2 hours longer than Daniel."
(d+2) = time required by Ben
Let the completed job = 1
:
After Ben had been working for 1 hour Daniel joined him and they completed the remaining portion of the job for 3 hours. "
Ben worked 4 hrs, Daniel worked 3 hrs
:
A shared work equation
4%2F%28%28d%2B2%29%29 + 3%2Fd = 1
multiply equation by d(d+2)
4d + 3(d+2) = d(d+2)
4d + 3d + 6 = d^2 + 2d
7d + 6 = d^2 + 2d
form a quadratic equation on the right
0 = d^2 + 2d - 7d - 6
d^2 - 5d - 6 = 0
Factors to
(d-6)(d+1) = 0
the positive solution
d = 6 hrs Daniel working time alone
and obviously
8 hrs Ben working alone
:
;
check
4%2F8 + 3%2F6 = 1