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?
:
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
:
{{{6/(t+5)}}} + {{{6/t}}} = 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