Can you tell me how to find the answer to this word problem

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

THE ANSWER IS: 2 hours and 24 minutes

BUT HOW WAS THIS PROBLEM SOLVED? WHAT STEPS DO I TAKE TO FIND THIS ANSWER?

If Sally can paint the house in 4 hours, then in 1 hour she can paint 1/4 of the house.
If John can paint the house in 6 hours, then in 1 hour he can paint 1/6 of the house.

Let x = the number of hours it will take them painting together

Then their combined rate = (1 house)/(x hours) or 1/x house/hr

To form the equation:

Sally's rate + John's rate = their combined rate

1/4 + 1/6 = 1/x

4/24 + 6/24 = 1/x

10/24 = 1/x

x = 24/10

= 2.4 hours

=2 hours and 24 min ( since24/60 = .4)

Answer: 2.4 hours or 2 hours 24 minutes

job=rate*time

In this case, job=1 house, and time for Sally=4 hours, and time for John=6 hours.

Then Sally's rate is 1/4 and John's rate is 1/6 because you can rearrange job=rate*time to get job/time=rate.

We can write this equation, where t=time it takes for both of them to paint the house together:
(1/4+1/6)t=1
(5/12)t=1
t=12/5 hours
12/5 hours = 2 2/5 hours = 2 hours and (2/5)60 minutes
= 2 hours and 24 minutes