Can someone tell me how to go about solving this word problem?

Question

If Sally can paint a house in 4 hours, and John can paint the same house in 6 hours, how long will it take for both of them to paint the house together??

Please don't put only the answer - I need to know how to solve it.
Thanks!!!

sorry guys, the answer isn't 5 hours. It's 2 hours and 24 minutes. But I need to know how to solve it. Help!!!

Answer 1

First, it is not an average like other posters suggest. Does it really make sense that TWO people can do the job in LONGER than it does ONE? (5 hours vs. 4 hours) No.

So...

let x = number of hours to paitn together

so x/4 is fraction of the job by sally and x/6 is the fraction of the job by john, together they do 1 job.

x/4 + x/6 = 1

Multiply through by 12 to remove fractions

3x + 2x = 12

5x = 12

x = 12/5 hours, or 2.4 hours, or 2 hrs 24 min

Answer 2

It will take 3 hours. Sally's half will take 2 hours (1/2 house of 4 hours=2). John would have taken 3 hours to paint his half(1/2 of 6).
Unless Sally picks up Johns slack and helps him paint some of his half then he might decide to take a break and Sally will finish his work , knowing if you want something done right do it yourself.

The answer is not 5 hours, it will not take longer than 4 hours because Sally can do it herself in 4.
Typical of a woman :)
I think Grover's Algebra equation is right

Answer 3

The answer should be 5. Basically it is asking for the average. So 4 + 6 =10 hours and you divide by 2 because that's 2 people so 10/2 is 5. So that means they can paint the house in 5 hours together.

Answer 4

Sally can paint the house in 4 hours.Therefore in 1 hour she can do 1/4 part of the job.Again John can paint the house in 6 hours.kSo in 1 hour ,he can do 1/6 part of the job.Therefore, together they can do 1/4 +1/6 =5/12 part of the job in 1 hour.Therefore .together they can do the job in (1)/(5/12) or 12/5 or 2 2/5hours or 2 hours 24 minutes.[2/5 hr=2/5multiplied by 60 or24 minutes]

Answer 5

I would add the 4 hours it takes Sally to the 6 hours it takes John and divide by the two painters to get an answer of 5 hours.

4 + 6=10 divided by 2 =5 hours

Answer 6

sally can paint half a house in two hrs and john can do half in 3, so 5. or add the two numbers 4+6 and divide by two

edit
wait that doesn't make sense. when sally is done her half she isn't going to stop. after two hrs sally has done half and john has done one third 1/2 +1/3 = 5/6 leaving 1/6 ........nevermind I retract my answer I don't know.

Grover why was x/4 + x/6 equal to 1?

Thank you Grover!

Answer 7

You take the 2 peeople and add them together. So Sally is 4 hours and John is 6. Once you add them that is 10. Divide by two to get that average and Viola! It wouild take them 5 hours. :]