SOLUTION: One conveyor belt can move 1000 boxes in 12 minutes. Another can move 1000 boxes in 9 minutes. If another conveyor is added and all three are used, the boxes are moved in 3 minut

Algebra ->  Rate-of-work-word-problems -> SOLUTION: One conveyor belt can move 1000 boxes in 12 minutes. Another can move 1000 boxes in 9 minutes. If another conveyor is added and all three are used, the boxes are moved in 3 minut      Log On


   

Question 33803: One conveyor belt can move 1000 boxes in 12 minutes. Another can move 1000 boxes in 9 minutes. If another conveyor is added and all three are used, the boxes are moved in 3 minutes. How long would it take the third conveyor belt alone to do the same job?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
1st belt Data:
time=12 min ; rate = 1/12 job/min
2nd belt Data:
time=9 min ; rate = 1/9 job/min
3rd belt Data:
time= x min ; rate = 1/x job/min
Together Data:
time= 3 min ; rate = 1/3 job/min
EQUATION:
rate + rate + rate= 1/3
1/12 + 1/9 + 1/x = 1/3
Multiply thru by 36x to get:
3x + 4x + 36 = 12x
5x=36
x=7.2 minutes (time for the 3rd belt working alone)
Cheers,
Stan H.