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 three-fifths 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 ÷ [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.

## Answer This Question

## Related Questions

- math - Mr.ariel and mr. Teddy are planning to paint tha house together.mr....
- math - A man can paint a fence in 8 hours. Another man can paint that fence in ...
- math - it takes bill 4 hours to paint a house. it takes john 7 hours to paint ...
- 12th grade - it takes bill 4 hours to paint a house. it takes john 7 hours to ...
- Algebra - If Sam takes 6 hours to paint a house, and Pat takes 12 hours to paint...
- algebra - It takes 7 hours for Will to paint a house. Judy can paint the same ...
- Math - Al can paint a room in a hours working alone. Bill can paint a room in b ...
- math - If Sally can paint a house in 4 hours, and John can paint the same house ...
- math - If Sally can paint a house in 4 hours, and John can paint the same house...
- math - If Sally can paint a house in 4 hours, and John can paint the same house ...

More Related Questions