Time and work

rawat2583 wrote:The minutes that it takes machine A to print n pages alone is half the minute that it takes machine B to print n pages alone. If machine A and machine B print n pages in 3 minutes when working together at their constant rates, respectively, in how many minutes machine B prints n pages alone?
A. 3.2 min B. 3.6 min C. 4.0 min D. 4.5 min E. 9.0 min

You can do this mathematically - if you suppose it takes t minutes for A to print n pages, you can then get the same time for each machine:

A prints 2n pages in 2t minutes
B prints n pages in 2t minutes

so A+B together print 3n pages in 2t minutes
and A+B together print n pages in 2t/3 minutes

Since 2t/3 = 3 , we have 2t = 9, and the question asked us to find B's time, which is 2t.

But we can avoid all that work -- only one answer choice makes any sense. If working together they need 3 minutes to print n pages, then alone, each of them of course takes longer than 3 minutes. Since B takes twice as long as A, if A takes more than 3 minutes, B takes more than 6 minutes, so only answer E could be right.