SOLUTION: Will can paint six rooms in twelve hours working alone. If his friend Matthew helps him, together they can paint the six rooms in seven hours. How long would it take Matthew to

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Will can paint six rooms in twelve hours working alone. If his friend Matthew helps him, together they can paint the six rooms in seven hours. How long would it take Matthew to       Log On


   

Question 720033: Will can paint six rooms in twelve hours working alone. If his friend Matthew
helps him, together they can paint the six rooms in seven hours. How long would
it take Matthew to paint the six rooms by himself?
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
The rates of any number of workers working together are additive. Use the idea, rate*time=jobs, the rate being jobs per time.

Will: 1 job per 12 hours, 1/12.
Matthew: r unknown.
Will plus Matthew: 1 job per 7 hours, 1/7.
Find Matthews work rate: 1%2F7=1%2F12%2Br.
r=1%2F7-1%2F12
r=%2812-7%29%2F84
r=5%2F84

Using the reciprocal, william would do 5 of these jobs in 84 hours, or the 1 job in 0.2%2A84 hours, 16.8 hours. About 16 hours and 45 minutes.