WORD PROBLEM: Sally and John panting a house together...

[MissieMousie]

I have many questions revolving around what I believe to be the rate=distance/time formula, but am uncertain what to do with it.

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?

Well, I set it up as follows:
S (represents Sally) and J (represents John);

S=x/4 and J=x/6. *lol*. I'm not sure what I am doing.

Any help would be appreciated.

MissieMousie

 

[Mrspi]

Re: WORD PROBLEM: Sally and John panting a house together..

I have many questions revolving around what I believe to be the rate=distance/time formula, but am uncertain what to do with it.

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?

Well, I set it up as follows:
S (represents Sally) and J (represents John);

S=x/4 and J=x/6. *lol*. I'm not sure what I am doing.

Any help would be appreciated.

MissieMousie

You're on the right track, but I definitely think it helps to specify what each variable used represents.

Let x = number of hours it takes them together

Sally does the whole job in 4 hours. In 1 hour, she does 1/4 of the job, and in x hours she does x/4 of the job.

John does the whole job in 6 hours. In 1 hour, he does 1/6 of the job, and in x hours, he does x/6 of the job.

Sally's part + John's part = whole job

(x/4) + (x/6) = 1

Multiply both sides of the equation by 12, the least common denominator of the fractions:

12(x/4) + 12(x/6) = 12(1)
3x + 2x = 12

Ok...can you take it from here?