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domster
06-27-2006, 08:16 PM
WORD PROBLEM:
WORKING ALONE COLEEN PAINTS A HOUSE 2 HOURS LESS THAN JAMES. TOGETHER THEY CAN PAINT THE HOUSE IN 10 HOURS. HOW LONG DOES JAMES TAKE TO PAINT THE HOUSE BY HIMSELF.

PLEASE SHOW ME HOW TO SOLVE. AN IMMEDIATE RESPONSE IS APPRECIATED.

pka
06-27-2006, 09:44 PM
If it takes James j hours to paint the house the each hour he paint \frac{1}{j} part of the house. Thus in any hour Colleen can paint \frac{1}{j-2} part of the house.

So together they can paint the house in 10 hours.

Thus we need to solve \left( {\frac{1}{j} + \frac{1}{{j - 2}}} \right)\left( {10} \right) = 1 for j.

Denis
06-27-2006, 09:57 PM
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:

stapel
06-27-2006, 11:34 PM
AN IMMEDIATE RESPONSE IS APPRECIATED.
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