the officejet printer can copy Janet's dissertation in 10 minutes. The laserjet printer can print the same copy in 20 minutes. If the two machines work together, how long would they take to copy the dissertation?
It would take 10 minutes.
rate office jet = 1copy/10 min
rate of laserjet = 1copy/20 min
combined rate = 1copy/10 + 1copy/20 = 3copy/20minutes
time for combined rate = 1 copy/(3copy/20min) = 20/3 minutes or
6 minutes, 40 seconds
To determine how long it would take for the two machines to copy Janet's dissertation when working together, we can calculate the inverse of their individual rates and sum them up.
Let's denote the rate at which the Officejet printer can copy the dissertation as "O", and the rate at which the Laserjet printer can copy the dissertation as "L". We can express these rates in terms of portions of the dissertation per minute:
O = 1/10 (as the Officejet printer takes 10 minutes to complete a copy)
L = 1/20 (as the Laserjet printer takes 20 minutes to complete a copy)
Now, we need to find the combined rate when both printers are working together. Adding their rates will give us the combined rate:
Combined rate = O + L = 1/10 + 1/20 = 2/20 + 1/20 = 3/20
The combined rate is 3/20 portions of the dissertation per minute. To find the time it would take for the two machines to copy the entire dissertation, we can invert this combined rate:
Time = 20/3 minutes
Therefore, when the Officejet and Laserjet printers work together, it would take approximately 6.67 minutes (or 6 minutes and 40 seconds) to copy the dissertation.