SOLUTION: Sally can paint a room in 4 hours. Joe can paint a room in 6 hours. HOw long will it take if they paint the room together? I tried averaging it (4+6)/2=5 but Sally can paint the

Question 325451: Sally can paint a room in 4 hours. Joe can paint a room in 6 hours. HOw long will it take if they paint the room together?
I tried averaging it (4+6)/2=5 but Sally can paint the room by herself in 4 hours, so this doesn't make sense.
Found 2 solutions by Alan3354, jim_thompson5910:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Maybe Sally and Joe find each other interesting, and it distracts them from painting? I've seen that happen.
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Sally does 1/4 room per hour.
Joe does 1/6 room per hour.
Add those, go from there.

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
I'm afraid it's not that simple.

If "Sally can paint a room in 4 hours", then she can paint of the room in 1 hour (divide each number by 4). So Sally's rate is of a room per hour. Likewise, since "Joe can paint a room in 6 hours", he can paint of the room in one hour. So his rate is of a room per hour.

Now add the two rates to get:

So their combined rate (if conditions are perfect) is rooms per hour. In other words, together they can paint of the room in one hour.

Now let 't' be the time that it takes them to complete the task. If we multiply the rate by the time 't', we will get a complete job. This is simply denoted by 1 (since we want to paint one room).

Basically, we then get the equation

Start with the given equation.

Multiply both sides by 12.

Multiply and simplify

Divide both sides by 5.

Simplify

So working together, they can paint 1 room in hours. Convert it to a mixed fraction to get . Finally, multiply by 60 (to convert it into minutes) to get . So or hours is 2 hours and 24 minutes.

So they can paint the room in 2 hours and 24 minutes.
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