Posted by Ashley on Monday, August 1, 2011 at 6:04am.
Bryan and Kim are painting a house. Working together they can paint a house in threefifths the time it takes Kim to paint the house working alone. Bryan takes 15 hours to paint the house alone. How long does it take Kim to paint the house working alone?

Math  Reiny, Monday, August 1, 2011 at 8:06am
let Kim's time working alone be x hrs
then Kim's rate = job/x
Brian's rate = job/15
combined rate = job/x + job/15 = job(x+15)/(15x)
time taken working together = job รท [job(x+15)/(15x)]
= 15x/(x+15) hrs
but 15x/(x+15) = (3/5)x
3x^2 + 45x = 75x
3x^2  30x = 0
3x(x  10) = 0
x = 0 or x = 10, but clearly x > 0
so x = 10
It would take kim 10 hours to work alone.
check: combined rate = job(1/10 + 1/15) = job(1/6)
so the combined time = 6/1 = 6 hours
what is 3/5 of 10 ?
yes, 6 hours.
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