The officejet printer can copy Sue's dissertation in 18 min. The laserjet printer can copy the same document in 22 min. If the two machines work together how long would they take to copy the dissertation?

Any help would be greatly appreciated.

In 18*22min, laserjet can do 22, and the officejet can do 18. So the rate is

rate= number/time= (18+22)/22*18=40/396min = 1dissertation/9.9 min

that answers it, but formally
dissertations= rate*time

time= dissertations/rate= 1dissertation/(1dissertation/9.9min)= 9.9 min

Would it be 99/10?

Thank you for your help.

yes, but few folks say 99/10 min, most would say 9.9 minutes, or 9 minutes 54seconds.

To find out how long it would take for the two printers to copy the dissertation if they work together, we can use the concept of rates.

First, let's determine the rates of each printer. The officejet printer can copy the dissertation in 18 minutes, so its rate is 1/18 dissertations per minute. Similarly, the laserjet printer can copy the dissertation in 22 minutes, so its rate is 1/22 dissertations per minute.

To calculate the combined rate when the two printers work together, we simply add their rates. So, the combined rate of the two printers is (1/18 + 1/22) dissertations per minute.

To determine the time it would take to copy the dissertation when the two printers work together, we can take the reciprocal of the combined rate. Therefore, the time it would take for them to complete the task is (1 / (1/18 + 1/22)) minutes.

We can simplify this expression by finding the least common multiple (LCM) of 18 and 22, which is 198. Multiplying 18 and 22 by their respective LCM, we get 198/18 and 198/22.

Thus, the time it would take for the two printers to copy Sue's dissertation when working together is:

(1 / (198/18 + 198/22)) minutes

Simplifying the expression further:

(1 / (11 + 9)) minutes
(1 / 20) minutes

Therefore, it would take the two printers 1/20 of a minute or 3 seconds to copy Sue's dissertation when working together.