Question

One conveyor belt can move 1000 boxes in 9 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

Answer:

It would take 7.62 minutes for the third conveyor belt alone to do the same job

Step-by-step explanation:

The together rate is the sum of each separate rate.

In this question:

First conveyor: Rate of 1/9.

Second: Rate of 1/11.

Third: Rate of 1/x.

Total: 1/3

So

$\frac{1}{9} + \frac{1}{11} + \frac{1}{x} = \frac{1}{3}$

$\frac{11x + 9x + 99}{99x} = \frac{1}{3}$

$\frac{20x + 99}{99x} = \frac{1}{3}$

$3(20x + 99) = 99x$

$60x + 297 = 99x$

$39x = 297$

$x = \frac{297}{39}$

$x = 7.62$

It would take 7.62 minutes for the third conveyor belt alone to do the same job