The officejet printer can copy sues dissertation in 16 minutes. The laser printer can copy the same document in 22 minutes. If the two machines work together, how long would they take to copy the dissertation?
rate of first copier = job/16
rate of 2nd copier = job/22
combined rate = job/16 + job/22 = job(19/176)
time at combined rate = job/(19job/176) = 176/19
or 9.26 minutes.
To find out how long it would take for the two machines to copy Sue's dissertation when working together, we need to calculate their combined rate of work.
Let's start by determining how much work each machine can complete in one minute.
The officejet printer can copy the dissertation in 16 minutes, which means it completes 1/16th of the work in one minute.
Similarly, the laser printer can copy the same document in 22 minutes, completing 1/22nd of the work in one minute.
Now, to find the total work completed by both machines working together, we add their individual rates of work:
1/16 + 1/22 = (22 + 16) / (16 * 22) = 38 / 352.
So, when the officejet and laser printer work together, they complete 38/352 of the work in one minute.
To find the time required to complete the entire dissertation, we divide the total work (1, representing the whole task) by their combined rate of work:
1 / (38/352) = 352 / 38 ≈ 9.26 minutes.
Therefore, the officejet printer and laser printer would take approximately 9.26 minutes to copy the dissertation when working together.