<PRE><B>Question 630704</B>
Christopher can paint the interior of his house in 15 hours.
 If he hires Cynthia to help him, they can do the same job together in 9 hours.
 If he lets Cynthia work alone, how long will it take her to paint the interior of his house?
:
Let c = time required by Cynthia alone
let the completed job = 1 (a painted house)
:
Each will do a fraction of the job. The two fractions add up to one.
:
A shared work equation
{{{9/15}}} + {{{9/c}}} = 1
Reduce fraction
{{{3/5}}} + {{{9/c}}} = 1
Multiply by 5c, resulting in:
3c + 5(9) = 5c
45 = 5c - 3c
45 = 2c
c = 45/2
c = 22.5 hrs, Cynthia alone
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:
Check this on a calc
9/15 + 9/22.5 =
.6 + .4 = 1</PRE>