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

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

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

`(1)/(9) + (1)/(11) + (1)/(x) = (1)/(3)`

`(11x + 9x + 99)/(99x) = (1)/(3)`

`(20x + 99)/(99x) = (1)/(3)`

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

`60x + 297 = 99x`

`39x = 297`

`x = (297)/(39)`

`x = 7.62`

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