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

1/b = 1/22 + 1/18

b = 22*18/(22+18) = 9.9 min

To find out how long it would take for the two machines to print the document together, we need to determine their combined rate of printing.

First, let's find out the rate of each printer individually. We can calculate this by dividing the number of documents each printer can copy by the time it takes.

For the officejet printer:
Rate of officejet printer = 1 dissertation / 22 min = 1/22 dissertation per minute.

For the laserjet printer:
Rate of laserjet printer = 1 dissertation / 18 min = 1/18 dissertation per minute.

To find the combined rate of the two printers, we add their rates together:

Combined rate = Rate of officejet printer + Rate of laserjet printer = 1/22 + 1/18 dissertation per minute.

To calculate this, we need to find a common denominator for the fractions. In this case, the least common multiple (LCM) of 22 and 18 is 198.

Combined rate = (9/198 + 11/198) dissertation per minute = 20/198 dissertation per minute.

So, the combined rate is 20/198 dissertation per minute.

To determine how long it would take for the two printers to print the document, we can calculate the reciprocal of the combined rate:

Time = 1 / Combined rate = 1 / (20/198) minutes.

To divide by a fraction, we multiply by the reciprocal of the fraction:

Time = 1 * (198/20) minutes = 9.9 minutes.

Therefore, it would take approximately 9.9 minutes for the officejet and laserjet printers to print the document together.