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

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> 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       Log On


   

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) About Me  (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) About Me  (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 1%2F4 of the room in 1 hour (divide each number by 4). So Sally's rate is 1%2F4 of a room per hour. Likewise, since "Joe can paint a room in 6 hours", he can paint 1%2F6 of the room in one hour. So his rate is 1%2F6 of a room per hour.


Now add the two rates to get: 1%2F4%2B1%2F6=3%2F12%2B2%2F12=5%2F12


So their combined rate (if conditions are perfect) is 5%2F12 rooms per hour. In other words, together they can paint 5%2F12 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 5%2F12 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 %285%2F12%29t=1


%285%2F12%29t=1 Start with the given equation.


cross%2812%29%285%2Fcross%2812%29%29t=1%2A12 Multiply both sides by 12.


5t=12 Multiply and simplify


%28cross%285%29t%29%2Fcross%285%29=12%2F5 Divide both sides by 5.


t=12%2F5 Simplify


So working together, they can paint 1 room in t=12%2F5 hours. Convert it to a mixed fraction to get 12%2F5=2%262%2F5. Finally, multiply 2%2F5 by 60 (to convert it into minutes) to get 60%282%2F5%29=120%2F5=24. So 12%2F5 or 2%262%2F5 hours is 2 hours and 24 minutes.


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