View Full Version : Algebra word problem: how long to paint the house himself?

domster

06-27-2006, 07:16 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.

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, 08:57 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, 10:34 PM

AN IMMEDIATE RESPONSE IS APPRECIATED.

If you are needing immediate and complete solutions, rather than tutoring (learning) help whenever our volunteers are able to stop by, then you might want to consider contracting with a fee-based service.

Otherwise, you will generally need to show some effort, and then please allow a few hours (or days) for an online reply.

Thank you for your consideration.

Eliz.

Powered by vBulletin® Version 4.2.2 Copyright © 2014 vBulletin Solutions, Inc. All rights reserved.