SOLUTION: Patrice, by himself, can paint a house in 10 hours. If he hires April to help, they can do the same job together in 6 hours. If he lets April work alone, how long will it take her

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Patrice, by himself, can paint a house in 10 hours. If he hires April to help, they can do the same job together in 6 hours. If he lets April work alone, how long will it take her       Log On


   

Question 781647: Patrice, by himself, can paint a house in 10 hours. If he hires April to help, they can do the same job together in 6 hours. If he lets April work alone, how long will it take her to paint the same house?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Patrice rate is 1/10 jobs per hour
April AND Patrice Together rate is 1/6 jobs per hour.

If assign C = 1/6, the Combined rate, and P = 1/10, Patrice's rate, then A is an unknown rate for April, then:
A%2BP=C
A%2B1%2F10=1%2F6
A=1%2F6-1%2F10
A=10%2F60-6%2F60
A=4%2F60
A=1%2F15-----unit is houses per hour.
This means, April paints the house by herself in 15 hours.