SOLUTION: 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 25 minutes to send out the email. H

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Question 1162966: 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 25 minutes to send out the email. How long will it take the newer computer to send out the email on its own?
Do not do any rounding.
Found 3 solutions by josgarithmetic, ikleyn, greenestamps:
Answer by josgarithmetic(39617) About Me  (Show Source):
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                RATE      TIME           JOBS

Old Computer                2x            1

New Computer                 x            1

Combined         1/25

The combined rate for the two together, being 1 job in 25 minutes, is
1%2F2x%2B1%2Fx=1%2F25.
Solve.

Answer by ikleyn(52781) About Me  (Show Source):
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.

Let x be the rate of work of older computer.


Then the rate of work of newer computer is 2x, according to the condition.


The combined rate of work of the two computers is x + 2x = 3x.


It means that  3x = 1%2F25;  hence,   x = 1%2F75 of the job per minute. 


It means the older computer will make the entire job in  75 minutes.


Therefore, the newer computer will do the job in  75%2F2 = 37 minutes and 30 seconds.    ANSWER

Solved.

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Another (mental) solution is like this . . .

The newer computer works as fast as two older computers.

Together, the older and the newer computer work as 3 (three) older computers.

Since they do the job in 25 minutes, it is the same as to say that three older computers make the job in 25 minutes.

Hence, one older computer makes the job in 3*25 = 75 minutes.

It implies that the newer computer will complete the job in 75/2 = 37 minutes and 30 seconds.


Explained with the same answer.



Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


A variation on the alternative mental solution provided by tutor @ikleyn....

Since the newer computer works twice as fast as the older, when doing the job together in 25 minutes the newer computer does 2/3 of the job.

If it takes the newer computer 25 minutes to do 2/3 of the job, it will take it (3/2)*25 = 37.5 minutes to do the whole job.

ANSWER: 37 1/2 minutes