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#1 2006-09-21 06:31:46

Beth
Guest

word problem - algebra

How do you solve the following type of word problem:

If Jane can paint a house in 2 days, Paul can paint the same house in 5 days and Mike can paint the same house in 3 days, how fast can they paint the house all working together?

Thank you.
Beth

#2 2006-09-21 06:38:17

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: word problem - algebra

Work out how much of a house they can each paint in one day.

Jane can paint a house in 2 days, and so can paint half a house in one day.
Similarly, Paul and Mike can paint a fifth and a third of a house respectively in one day.

That means that combined, they can paint 1/2 + 1/5 + 1/3 of a house in one day.

This works out to be 15/30 + 6/30 + 10/30 = 31/30 of a house.
This in turn means that they can paint one house in 30/31 days. (Or just under one.)


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#3 2006-09-21 06:40:35

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,562

Re: word problem - algebra

I've seen this problem before.  I think reciprocals is one way to do it.
How much of the house can each get done in one second??
Add the 3 parts of a house per second together to get their total parts of a house per second.
Then say they together paint 1/1000 of a house in one second.
Then they paint the whole house in 1000 seconds, the reciprocal.
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