SOLUTION: A and B can complete a work in 2 and 6 days respectively. If C alone can complete the work in 3 days, in how many days can they complete the same work, if all three work together

Question 681057: A and B can complete a work in 2 and 6 days respectively. If C alone can complete the work in 3 days, in how many days can they complete the same work, if all three work together
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Let x=amount of time it takes all three working together to complete the work
Then all three works at the rate of 1/x of the work per day
A works at the rate of 1/2 of the work per day
B works at the rate of 1/6 of the work per day
C works at the rate of 1/3 of the work per day
Sooooo
1/2 + 1/6 + 1/3=1/x Multiply each term by 6x
3x+x+2x=6
6x=6
x=1 hr-----------------time it takes all three working together to complete the work
CX
In 1 hr A completes 1/2 of the work
In 1 hr B completes 1/6 of the work
In 1 hr C completes 1/3 of the work
1/2+1/6+1/3=1 (1 work, that is)
3/6+1/6+2/6=1
1=1
Hope this helps---ptaylor
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