<PRE><B>Question 486794</B>
Working together, two men can do a job in 20 days. 
Working alone, however, it would take one man 9 days longer than it would take the other to complete the job.
 How long would it take each separately?
:
Let t = time required by the 1st man to do the job alone
then
(t+9) = time required by the 2nd man alone
:
Let the completed job = 1
:
A typical shared work equation
:
Each man will do a fraction of the job, the two fractions add up to 1
:
{{{20/t}}} + {{{20/(t+9)}}} = 1
:
multiply by t(t+9), results
20(t+9) + 20t = t(t+9)
20t + 180 + 20t = t^2 + 9t
:
Arrange as a quadratic equation
t^2 + 9t - 40t - 180 = 0
t^2 - 31t - 180 = 0
:
you can solve this using the quadratic equation, but it will factor to:
(t-36)(t+5) = 0
:
the positive solution
t = 36 days required by the 1st man
then
36 + 9 = 45 days required by the 2nd man
:
:
Check this
20/36  + 20/45
.56 + .44 = 1
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