Question

It takes an older computer twice as long to send out a company's email as it does a newer computer. working together, it takes the two computers 5 minutes to send out the email. how long will it take the newer computer to send out the email on its own?

Answer 1

7.5 minutes

Explanation:

You want the time it takes a newer computer to do a job that gets done in 5 minutes when the new computer works with one that takes twice as long.

Setup

Let n represent the number of minutes it takes the new computer to do the job. Then it completes 1/n of the job in each minute. If it takes the older computer 2n minutes to do the job, then that computer completes 1/(2n) of the job in each minute.

Together the two computers complete 1/5 of the job in each minute:

1/n + 1/(2n) = 1/5

Solution

Multiplying by 5n gives ...

5 + 5/2 = n

15/2 = 7.5 = n

The newer computer can complete the job on its own in 7.5 minutes.

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Additional comment

Rates in the form job/time will add when the work is done in parallel (simultaneously). If the work is done in series (sequentially), then the times in the form time/job will add.

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