SOLUTION: Ethan can paint a room in eleven hours. Victoria can paint the same room in twelve hours. How long does it take for both Ethan and Victoria to paint the room if they are working to

Question 246480: Ethan can paint a room in eleven hours. Victoria can paint the same room in twelve hours. How long does it take for both Ethan and Victoria to paint the room if they are working together?

Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!

Let x=amount of time it takes if both are working together
Then together they paint at the rate of 1/x room per hour
Ethan paints at the rate of 1/11 room per hour
Victoria paints at the rate of 1/12 room per hour
Together, they paint at the rate of 1/11 + 1/12 room per hour
So our equation to solve is:
1/11 + 1/12=1/x

multiply each term by 132x
12x+11x=132
23x=132 divide each side by 23
x= 132/23 or 5.739 hours
CK
Ethan in 5.739 hours paints (1/11)*(132/23)= 12/23 of the room
Victoria in 5.739 hours paints (1/12)*(132/23)=11/23 of the room
12/23 + 11/23=23/23 or 1 room

Hope this helps---ptaylor
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