SOLUTION: Christopher can paint the interior of his house in 21 hours. If he hires Cynthia to help him they can do the same job together in 15 hours. If he lets Cynthia work alone, how long

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Christopher can paint the interior of his house in 21 hours. If he hires Cynthia to help him they can do the same job together in 15 hours. If he lets Cynthia work alone, how long       Log On


   

Question 258585: Christopher can paint the interior of his house in 21 hours. If he hires Cynthia to help him they can do the same job together in 15 hours. If he lets Cynthia work alone, how long will it take her to paint the interior of his house?
Enter the exact answer.

Cynthia can paint the house alone in hours.

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Christopher can paint the interior of his house in 21 hours.
If he hires Cynthia to help him they can do the same job together in 15 hours.
If he lets Cynthia work alone, how long will it take her to paint the interior of his house?
:
Let x = time required by Cynthia, alone
:
Let the completed job = 1
Each painter will do a fraction of the job, the two fractions add up to 1
:
A typical shared work equation
15%2F21 + 15%2Fx = 1
Multiply by 21x, to get rid of the denominators, results
15x + 21(15) = 21x
:
15x + 315 = 21x
:
315 = 21x - 15x
:
315 = 6x
x = 315%2F6
x = 52.5 hrs by herself
;
:
Check this on a calc
15/21 + 15(52.5) =
.714 + .286 = 1