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. 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?

Respuesta :

aaisrakh

Answer:

85 bolts.

Step-by-step explanation:

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

[tex]R = \frac{work}{time}[/tex]. If your problem has multiple machines working together to complete a job, you should sum their work rates:

[tex]R_{A}+R_{B}+R_{C}+...[/tex]  

In the problem given:

[tex]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}[/tex]

To solve the equation system for [tex]R_{B}[/tex], you could subtract the first and last equations:

[tex]R_{A}+R_{B}+R_{C}=287\\- (R_{A}+R_{B}=202)\\\\[/tex]

Then, [tex]R_{C}=287 - 202 = 85 \frac{bolts}{h}[/tex].