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**Beth****Guest**

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

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

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.)

Why did the vector cross the road?

It wanted to be normal.

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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,552

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.

I gotta run, and go for a bike ride to lose weight, so someone else will help you more...

**igloo** **myrtilles** **fourmis**

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