Question 542446
<br><font face="Tahoma">This is a fairly standard "rate of work" problem.<br>

The standard way to solve these is using this formula:<br>

{{{1/A+1/B=1/T}}}<br>

where A is the time taken by A, B is the time taken by B, and T is the time taken when they work together.<br>

This can also be extended to more than two different workers, machines, etc.<br>

So in our case, time A is 15, and time B is 12.  Let's solve:<br>

{{{1/15+1/12=1/T}}}<br>

Find a common denominator of 15 and 12 (it's 60):<br>

{{{4/60+5/60=1/T}}}<br>

{{{9/60=1/T}}}<br>

{{{9*T=60}}}<br>

{{{T=20/3}}} which is about 6.667 minutes which makes sense!<br>

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More information:<br>

Notice that we didn't use the fact about the 300 pages?<br>

The important thing is that copier A and B both did the exact same job.<br>

We would have a LITTLE more work to do if the jobs were different.<br>

In that case we would just need to convert one of the jobs so that it was the equivalent of the other one.<br>

For example if it said copier A did 300 pages in 12 minutes, and copier B did 900 pages in 60 minutes,<br>

we would need to convert A to 900 pages, or convert B to 300 pages.<br>

I would convert copier A to 900 pages by multiplying both values by 3.<br>

Hence, copier A could do 900 pages in 36 minutes.<br>

Then we could proceed with the problem once again as we did above.<br>

I hope this helps!