## anonymous 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?

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.