SOLUTION: matt and jeff need to paint a fence. matt can do the job alone 8 hours faster than jeff. if together they work for 19 hours and finish only 7/8's of the job how long would jeff nee

Question 400936: matt and jeff need to paint a fence. matt can do the job alone 8 hours faster than jeff. if together they work for 19 hours and finish only 7/8's of the job how long would jeff need to do the job alone?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
matt and jeff need to paint a fence.
matt can do the job alone 8 hours faster than jeff.
if together they work for 19 hours and finish only 7/8's of the job how long
would jeff need to do the job alone?
:
Let t = Jeff's time working alone
then
(t-8) = Matt's time to do the job alone
:
Let the completed job = 1
:
The equation to complete 7/8 of the job
+ =
multiply equation by 8t(t-8); results
19(8(t-8)) + 19(8t) = 7t(t-8)
152t - 1216 + 152t = 7t^2 - 56t
304t - 1216 = 7t^2 - 56t
Arrange as a quadratic equation
7t^2 - 56t - 304t + 1216 = 0
7t^2 - 360t + 1216 = 0
Solve this equation using the quadratic formula

:
the reasonable solution: t = 47.79 hrs is Jeff's time alone
:
Jeff has to do 1/8 of the job alone; let j = time to do this
=
8j = 47.79
j =
j = 5.97 hrs for Jeff to finish the job
;
:
Check this (Matt's time 47.79-8 = 39.79)
+ + =
.477 + .398 + .125 = 1; confirms our solution

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