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  • 5 years ago

one conveyor belt can move 1000 boxes in 7 minutes. another can move 1000 boxes in 11 minutes. if another conveyor belt 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?

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  1. anonymous
    • 5 years ago
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    You are trying to find the speed of the third conveyor belt. So, the speed of the first one is: $$\frac{1000\textrm{ boxes}}{7\textrm{ min}} = \frac{1000}{7} \textrm{boxes/min}$$ Likewise for the second one: $$\frac{1000\textrm{ boxes}}{11\textrm{ min}} = \frac{1000}{11} \textrm{boxes/min}$$ And you know the total speed is: $$\frac{1000\textrm{ boxes}}{3\textrm{ min}} = \frac{1000}{3} \textrm{boxes/min}$$ The total speed has to be the sum of the three conveyor belt speeds, so you have: $$\textrm{(speed of conveyor belt 1)} + \textrm{(speed of conveyor belt 2)} + x = \textrm{total speed}$$ To find your answer, you therefore need to solve the equation: $$\frac{1000}{7} + \frac{1000}{11} + x = \frac{1000}{3}$$ The rest is left as an exercise for the reader. Also, your teacher is mean for giving your three prime numbers in this problem.

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