SOLUTION: Conveyor belt # 1 can move 1,000 boxes in 8 minutes. Conveyor belt #2 can move 1,000 boxes in 7 minutes. If conveyor belt #3 is added and all three are used, the 1,000 boxes are mo

Question 1154304: Conveyor belt # 1 can move 1,000 boxes in 8 minutes. Conveyor belt #2 can move 1,000 boxes in 7 minutes. If conveyor belt #3 is added and all three are used, the 1,000 boxes are moved in 3 minutes. How long would it take the third conveyor belt alone to do the same job? Round to the nearest whole number if necessary.
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!

let us assume moving 1000 boxes is 1 job
Conveyor belt # 1 can move 1,000 boxes in 8 minutes.
so it does 1/8 of the job in 1 min
Conveyor belt #2 can move 1,000 boxes in 7 minutes.
In 1 minute it will move 1/7 of the job
If conveyor belt #3 is added and all three are used,
the 1,000 boxes are moved in 3 minutes.
in 1 minute all three move 1/3 of the job

let the third take x hours to do the job alone
it does 1/x of the job in 1 min
1/x+1/7+1/8 = 1/3
1/x = 1/3-(1/7+1/8)
1/x = 0.065
x = 15.27 hours

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