A new copy machine works three times faster than the older model. It takes 12 minutes to complete a job when both machines are working together. Find the time required for the new copy machine to complete the job by itself.

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A new copy machine works three times faster than the older model. It takes 12 minutes to complete a job when both machines are working together. Find the time required for the new copy machine to complete the job by itself.

The new machine is 3 times as fast, so we have 3/t.

\(\displaystyle \frac{1}{t}+\frac{3}{t}=\frac{1}{12}\)

Solve for t.

You can do the other problem in a similar manner.

Let time it takes for new machine to do the job alone be called x minutes.

Then time it takes for old machine to do the job alone is 3x minutes.

The time it takes for them working together is 12 minutes.

In one minute new machine can do 1/x of the job.

In one minute old machine can do ____ of the job.

In one minute working together they can do ____ of the job.

Now, write your equation on basis that in one minute the amount of job new machine does added to the amount of job the old machine does equals the amount of the job done by their working together.

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1/t+3/t=1/12

=4/t=1/12

4/t x 4=t

1/12 x 4 = 4 4/12

t=4 4/12

but i advise someone look over my answer so you wont get it wrong i hope i was some kind of help

There are some errors in your arithmetic (you really have to be more careful, foothill), but also I want you to think logically about what this answer means. If both machines complete the task in 12 minutes when they're both working on the task together, how could just the one machine (the old one at that) complete it in under 5 minutes?foothillstudent_12 said:hi My name is De Shaun and i am new to this website but i think i can help you, now mind you i am not a genius so it might not be right but it's worth a try

1/t+3/t=1/12

=4/t=1/12 >>> Or, just cross multiply here... 48 = 1t

4/t x 4=t >>> (4/t) (t) would equal 4, but (4/t)(4) = 16/t

1/12 x 4 = 4 4/12 >>> Actually it equals 4/12, without the whole number, but that's beside the point.

t=4 4/12

but i advise someone look over my answer

Once you get the answer, take a step back and figure out if it makes any sense. If it doesn't make sense in the context of the problem, something's wrong. In your case, there are too many "4"s floating around in your arithmetic. But that problem can be fixed. As for the logic flaw, you just have to remember that you're working on real problems here, not just manipulating some numbers.

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