Question

. In a factory there are three machines, A, B, and C. When all three machines are working, they produce 287 bolts per hour. When only machines A and C are working, they produce 197 bolts per hour. When only machines A and B are working, they produce 202 bolts per hour. How many bolts can machine B produce per hour?

Answer 1

85 bolts.

Explanation:

The work rate of a machine is given by the job completed per time:

`R = (work)/(time)`. If your problem has multiple machines working together to complete a job, you should sum their work rates:

`R_(A)+R_(B)+R_(C)+...`

In the problem given:

`R_(A)+R_(B)+R_(C)=(287 bolts)/(h)\\ R_(A)+R_(C)=(197 bolts)/(h) \\R_(A)+R_(B)=(202 bolts)/(h)`

To solve the equation system for
`R_(B)`, you could subtract the first and last equations:

`R_(A)+R_(B)+R_(C)=287\\- (R_(A)+R_(B)=202)\\\\`

Then,
`R_(C)=287 - 202 = 85 (bolts)/(h)`.