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Question 957219: Alvin, Betty, and Charlie want to paint a living room. Alvin could paint the room in 3 hours if he worked by himself. Betty could do it in 4 hours by herself, and Charlie would take 8 hours if working by himself. If they all work together and don’t get in each other’s way, how long will the job take?
Answer by addingup(3677)   (Show Source):
You can put this solution on YOUR website! Let's call the time it takes them together x. And let's bring them all to one hour: Alvin can do a room in 3 hours, in 1 hour he can do 1/3. Betty 1/4 and Charlie 1/8.
1/3x+1/4x+1/8x= 1 hour. Let's find a LCD so we can add them up:
1/3: 3 is a prime number, it cannot be broken down any more, so here we get 3.
1/4: 4= 2*2
1/8: 8= 2*2*2 These three 2's account for the two 2's above. We have to account for the 3 from 1/3:
2*2*2*3 = 24 is the LCD for these 3 numbers. We will multiply everything, both sides of the equation, times 24:
24/1*1/3= (24*1)/(1*3)= 24/3 Divide, 3 goes 8 times into 24: 24/3= 8
Do the same for 1/4: 24*1/4 = 6 and 24*1/8= 3. And on the right, 1 x 24=24
Now we have that:
8x+6x+3x= 24 Add the x's
17x= 24 Divide both sides by 17
Together, it takes them:
x = 1.41 hours, or (.41 x 60= 24.6)1hour and 24.6 minutes, or (.6*60=36) 1 hour 24 minutes and 36 seconds (because remember that 1 hour = 60 minutes and 1 minute = 60 seconds).
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