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

Answer:

85 bolts.

Step-by-step explanation:

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

$R = \frac{work}{time}$. 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:

$R_{A}+R_{B}+R_{C}=\frac{287 bolts}{h}\\ R_{A}+R_{C}=\frac{197 bolts}{h} \\R_{A}+R_{B}=\frac{202 bolts}{h}$

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, $R_{C}=287 - 202 = 85 \frac{bolts}{h}$.