# This is a simple algebra question.

By mommaj

@mommaj (22768)

United States

August 13, 2009 3:46pm CST

If someone paints a house in 4 hours and someone else paints the house in 6 hours, if they work together how long will it take them to paint the house? Please explain your answer. I am baffled. OH, this is not a homework question. My husband said why would a painter that can work in 4 hours want to hire anyone who takes 6 hours. So that is not the answer either!

1 person likes this

4 responses

@KMilliron (20)

•

13 Aug 09

Our equation will be 1/4+1/6=1/x
1/4 and 1/6 being how much of a house each individual painter can do in one hour.
Now we must find our common denominator (12x) and multiply it through out.
Our equation now it 12x/4+12x/6=12x/x
Now we reduce
3x+2x=12
5x=12
x=2.4
It will take them 2.4 hours.
Ha ha. Math has always been my second best subject, glad I could refresh before school begins again.

@KMilliron (20)

•

13 Aug 09

Lets do it this way.
All we know is because Painter A is faster so the job will get done in AT LEAST four hours, but becuase Painter B is helping, it will get done in under that time.
Four and six's greatest common denominater is twelve, so we're going to divide twelve by four and again by six.
We now have three and two. Three plus two equals five. Now we take that common denominator (or any number really) and divide it by what we just came up with, the five.
We get 2.4
Lets try it with thirty six.
36/4=9 36/6=6
9+6=15
36/15= 2.4
That's kind of all I got, and I don't know how to explain how it works.
But if it helps...

@Canellita (12058)

• United States

29 Sep 09

Hmmmm... looks like I overlooked this one. Maybe the painter who paints in 4 hours wanted to drag the job out?

@sid556 (31005)

• United States

2 Sep 09

It has been years since i've done algebra. My guess and probably it's wrong is 5 hours. here is how I arrived at that. X=4, y=6. together they are 6+4=10. That is the amount of hours that they would work on the house if they were to do it alone. Divide that by 2 would be 5hours. That is my answer....am I right? Thanks for the brain excersise.

@mommaj (22768)

• United States

2 Sep 09

Saw your response that you saw the right answer above. Don't feel bad that was my reaction too. It's been a lot longer than five years since I did algebra, so maybe this is new math. HAHAHAHA. Just kidding. I would have to say the other guy even explained it halfway decently.

1 person likes this

@zeromidget2669 (183)

• United States

1 Oct 09

I would say it would take them about 3 hours to paint the house. Honestly I can't explain it. Ever since i read it, thats the only number thats stuck in my head lol. Is that right??