Question

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?

Answer 1

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.