Question

A new photocopier can make 72 copies in 2 min. When an older photocopier is operational, the two photocopiers together can make 72 copies in 1.5 min. How long would it take the older photocopier to make 72 copies working alone?

Answer 1

About 1/4 of the time, id think

Answer 2

6min

Answer 3

First, you want the speeds of the copiers in a single minute. So the one is easy. N for new and O for Old. N does 72 in 2 minutes, or 72/2=36. So say N=36. The old is unknown and part of what we need here.

Now, if we take what has been told to us, New+Old times one and a half minutes is 72 copies. Or:
1.5(N+O)=72
Well, we know N so:
1.5(36+O)=72

Now solve for O. Or use an x if that is easier to keep track of because O looks like 0.

Once you have the speed of the old copier, you need how long to get 72 copies. Well, T minutes times O = 72! So TO=72 means T=72/O. That is why finding the speed of the old is how you get the answer.

Answer 4

in 1 min old and new photocopier can make 72/1.5 =72/(3/2)=72*2/3=48copies
in 1 min new photocopier can make 72/2 =36copies
thus in 1 min old photocopier can make 48-36 = 12copies
thus for old photocopier to make 72 copies would take 72/12 =6 min (old working alone)

Answer 5

4x the time

Answer 6

In general, with these sorts of problems, the approach is to find the unit rate of making copies, filling swimming pools, draining tanks, etc.

Here, the new copier does 72 copies in 2 minutes, so 72 copies/2 minutes = 36 copies/minute. In 1.5 minutes it will do 1.5 minutes * 36 copies/minute = 54 copies. If the two copiers together do 72 copies in 1.5 minutes, that means the old copier did 72-54 = 18 copies in 1.5 minutes, or 18 copies/1.5 minutes = 12 copies/minute. For it to do the whole job would take it 3x as long (ratio of speeds is 36 copies/min / 12 copies/ min = 3 , or 72 copies/12 copies/minute = 6 minutes, which is 3x 2 minutes).