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September 23, 2014

September 23, 2014

Posted by **Ashley** on Monday, August 1, 2011 at 6:04am.

- Math -
**Reiny**, Monday, August 1, 2011 at 8:06amlet 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 ÷ [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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