work rate question

Question

In a photocopy center 2,070 pages need to be copied. Photocopy machine A is twice as fast as another photocopy machine B and when working together they can complete this job in half an hour. The two machines start copying and after 10 minutes a third photocopy machine C, which is as fast as A, is added in the work to speed up the process. How many minutes earlier will the job finish?

Answer 1

Since machine A is twice as fast as machine B, B makes 1/3 of the total copies made and A make 2/3.

In one hour the two machines together would make 4140 copies, i.e. A makes 2760 copies per hour and B makes 1380 copies per hour.

Machine C also makes 2760 copies per hr but works 1/6 of an hour less than the other 2, i.e.

(2760+1380)T + [T-(1/6)]2760 = 2080 where T is the time worked by the first 2 machine together.

6900T = 2070+460 = 2530 and

T = .366666666 hrs or 22 minutes, i.e. 8 minutes less by adding the 3rd machine.