Question

HELP
NEW PHOTOCOPIER CAN MAKE 72 COPIES IN 2 MINS. WHEN AN OLDER PHOTOCOPIER IS OPERATIONAL, THE TWO PHOTOCOPIERS TOGETHER CAN MAKE 72 COPIES IN 1.5 MINS. HOW LONG WOULD IT TAKE THE OLDER PHOTO COPIER TO MAKE 72 COPIES WORKING ALONE?

Answer 1

Explaining how this works is a real pain in person, let alone through text... but I can explain the pattern.
In these problems, there is always "a job".
There are two things that do the job (thing A and thing B).
Set-up this equation\[\frac{1}{time A}+\frac{1}{time B}=\frac{1}{time A and B}\] So by time A, I mean... the time it takes for one thing to do the job
time B is the time it takes the other thing to do the job and the last one is the time it takes to do them together.
I put it this way because sometimes they change what they give you versus what they want, but this covers it.

Answer 2

but theres not enough info to get an answer right.

Answer 3

In your case... either time A or time B your unknown (x)... then fill in the rest. I got an answer.

Answer 4

so 1/1.5 + 1/x =1/ 1.5x

Answer 5

close... 1/2 on the left side instead of 1/1.5

Answer 6

ok then i solve for x?

Answer 7

yes... I use an LCD method, but there are other ways.

Answer 8

easier ways?

Answer 9

oh wait... I just saw that you put x on the right side... it doesn't go there

Answer 10

\[\frac{1}{new}+\frac{1}{old}=\frac{1}{together}\]\[\frac{1}{2}+\frac{1}{x}=\frac{1}{1.5}\]

Answer 11

I like LCD because it is fast with few steps... but one other way would be to take fractions without x to the other side, find a common denominator, add them and then cross multiply the whole thing to get x out of the denominator.

Answer 12

im confused

Answer 13

Logic is simpler in this case... think about this:
How many pages per minute can the new printer do?

Answer 14

er... photocopier

Answer 15

39.5

Answer 16

If it can do 72 pages in 2 minutes, it can do half that in one minute... 36.

Answer 17

right. i was thinking 75.

Answer 18

How many pages per minute can be copied by them together?

Answer 19

72 in 1.5 mins so 48 per minute

Answer 20

yes!
So the new photocopier's rate is 36 pages per minute
together their rate is 48 pages per minute.
The old photocopier is what is making the difference between those two numbers, so what is the rate of the old photocopier?

Answer 21

12

Answer 22

yes!
how long will it take to copy 72 pages at 12 pages per minute?

Answer 23

6 mins

Answer 24

Yes! Now that was the logical way... it is a little trickier to know what to do and when, it is probably the first way that you'll be tested on.

Answer 25

yeah haha but now since i put the pieces together it makes sense

Answer 26

good

Answer 27

thanks

Answer 28

You're welcome