SOLUTION: Christopher can paint the interior of his house in 28 hours. If he hires Cynthia to help him, they can do the same job together in 20 hours. If he lets Cynthia work alone, how long

Question 988272: Christopher can paint the interior of his house in 28 hours. If he hires Cynthia to help him, they can do the same job together in 20 hours. If he lets Cynthia work alone, how long will it take her to paint the interior of his house?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Christopher can paint the interior of his house in 28 hours.
If he hires Cynthia to help him, they can do the same job together in 20 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 working alone
let the completed job = 1
:
Each will do a fraction of the job, the two fractions add up to 1
+ = 1
multiply by 28c, get rid of the denominators
28c* + 28c* = 28c
Cancel the denominators and we have
20c + 28(20) = 28c
560 = 28c - 20c
560 = 8c
c = 560/8
c = 70 hrs Cynthia working alone
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