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An old copying machine can produce 90 copies of a report in 120 minutes. A new machine can do the same job in 80 minutes. If both machines are used, how long would it take to do the job?

Answer :

Final answer:

The old machine produces 0.75 copies per minute and the new machine 1.125 copies per minute, giving a combined rate of 1.875 copies per minute. It would take both machines working together 48 minutes to produce 90 copies.

Explanation:

To determine how long it takes for both copying machines to produce the same number of copies when used together, we need to calculate their combined work rate. The old copying machine produces 90 copies in 120 minutes, which means its work rate is \0.75 copies per minute\. The new machine completes 90 copies in 80 minutes, which means its rate is \1.125 copies per minute\.

To find the combined rate, we simply add the individual rates of the machines:

  • Old machine: 0.75 copies/min
  • New machine: 1.125 copies/min
  • Combined rate: 0.75 + 1.125 = 1.875 copies/min

Now, to find out how long it would take for both machines to complete 90 copies together, we divide the total number of copies by the combined rate:

\Time\ = Total copies / Combined rate = 90 copies / 1.875 copies/min = 48 minutes

Therefore, it would take both machines 48 minutes to produce 90 copies when working together.

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