Algebra word problem: how long to paint the house himself?
- Thread starter domster
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pka
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Re: ALGEBRA WORD PROBLEM
If it takes James j hours to paint the house the each hour he paint \(\displaystyle \frac{1}{j}\) part of the house. Thus in any hour Colleen can paint \(\displaystyle \frac{1}{j-2}\) part of the house.
So together they can paint the house in 10 hours.
Thus we need to solve \(\displaystyle \left( {\frac{1}{j} + \frac{1}{{j - 2}}} \right)\left( {10} \right) = 1\) for j.
If it takes James j hours to paint the house the each hour he paint \(\displaystyle \frac{1}{j}\) part of the house. Thus in any hour Colleen can paint \(\displaystyle \frac{1}{j-2}\) part of the house.
So together they can paint the house in 10 hours.
Thus we need to solve \(\displaystyle \left( {\frac{1}{j} + \frac{1}{{j - 2}}} \right)\left( {10} \right) = 1\) for j.
c = Coleen; then James = c + 2
in 1 hour, portion of work done = 1/c + 1/(c+2) = (2 + 2c) / (c^2 + 2c)
so: (c^2 + 2c) / (2 + 2c) = 10
c^2 + 2c = 20 + 20c
c^2 - 18c - 20 = 0
Solve for c using quadratic; you'll get close to an integer answer.
EDIT: Geezzzz pka...didn't know you were there!
To domster: don't get confused; pka's and mine will give you same answer:
mine is better :roll:
in 1 hour, portion of work done = 1/c + 1/(c+2) = (2 + 2c) / (c^2 + 2c)
so: (c^2 + 2c) / (2 + 2c) = 10
c^2 + 2c = 20 + 20c
c^2 - 18c - 20 = 0
Solve for c using quadratic; you'll get close to an integer answer.
EDIT: Geezzzz pka...didn't know you were there!
To domster: don't get confused; pka's and mine will give you same answer:
mine is better :roll:
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- Feb 4, 2004
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