SOLUTION: Jeff takes 5 hr longer to build a fence than it takes Bill. When they work together, it takes them 6 hours. How long would it take Bill to do the job alone?
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Question 193360: Jeff takes 5 hr longer to build a fence than it takes Bill. When they work together, it takes them 6 hours. How long would it take Bill to do the job alone? Found 2 solutions by ankor@dixie-net.com, solver91311:Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! Jeff takes 5 hr longer to build a fence than it takes Bill. When they work together, it takes them 6 hours. How long would it take Bill to do the job alone?
:
Let t = B's time to build the fence alone
Then
(t+5) = J's time to build the fence alone
:
Let the completed job = 1
: + = 1
Multiply equation by t(t+5); results:
6t + 6(t+5) = t(t+5)
6t + 6t + 30 = t^2 + 5t
12t + 30 = t^2 + 5t
0 = t^2 + 5t - 12t - 30
A quadratic equation
t^2 - 7t - 30 = 0
Factors to:
(t-10)(t+3) = 0
The positive solution is what we want:
t = 10 hrs for Bill to do the job alone
;
;
Check solution (Jeff will take 15 hrs):
6/10 + 6/15 =
3/5 + 2/5 = 1
Working together, they can do the job in 6 hours which means that they can do of the job in 1 hour. Let x represent the number of hours it would take Bill to do the entire job by himself. Then he can do of the job in one hour. Likewise, Jeff can do of the job in one hour, and together they can do of the job in 1 hour.
Cross multiply and put the resulting quadratic into standard form:
Factor and solve. Exclude the negative root as extraneous.
