SOLUTION: Two workers finished a job in 7.5 days. How long would it take each worker to do the job by himself if one of the workers needs 8 more days to finish the job than the other worker?

Question 1019703: Two workers finished a job in 7.5 days. How long would it take each worker to do the job by himself if one of the workers needs 8 more days to finish the job than the other worker?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Two workers finished a job in 7.5 days.
How long would it take each worker to do the job by himself if one of the workers needs 8 more days to finish the job than the other worker?
:
let t = time required by one worker to complete the job alone
then
(t+8) = time required by the other worker (shirker)
:
let the completed job = 1
:
A typical shared work equation
+ = 1
multiply by t(t+8), cancel the denominators, and you have
7.5(t+8) + 7.5t = t(t+8)
7.5t + 60 + 7.5t = t^2 + 8t
15t + 60 = t^2 + 8t
form a quadratic equation on the right
0 = t^2 + 8t - 15t - 60
t^2 - 7t - 60 = 0
Factor easily to
(t-12) (t+5) = 0
the positive solution is all we want here
t = 12 days, the first guy working alone
then
the shirker would struggle thru the job in 20 days.
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