the officejet printer can copy lisa's dissertation in 18 min. the laserjet printer can copy the same document in 20 min. if the two machines work together, how long would the take to copy the dissertation
For every minute, the officejet does 1/18 of the work, while the laserjet does 1/20 of the work.
Together the two printers do (1/18+1/20)=19/180 of the work every minute.
If the two work together, and assuming the work can be shared to keep the two busy all the time, the work can be done in 1/(19/180) = 180/19 = 9.47 minutes.
time = 1/(1/18 + 1/20)
= 1/(19/180) = 180/19 = 9.47 minutes
To determine how long it would take for the Officejet and Laserjet printers to copy the dissertation when working together, we need to find their combined rate of work.
Let's calculate the rate of work for each printer first:
The Officejet can copy the dissertation in 18 minutes, so its rate of work is 1/18 dissertations per minute.
The Laserjet can copy the dissertation in 20 minutes, so its rate of work is 1/20 dissertations per minute.
Now, to find their combined rate of work, we add the rates of work of both printers:
1/18 + 1/20 = (20 + 18) / (18 * 20) = 38 / 360 = 1/9.47
So, working together, the Officejet and Laserjet printers have a combined rate of 1/9.47 dissertations per minute.
To find how long it would take them to copy the entire dissertation together, we can take the reciprocal of the combined rate of work:
1 / (1/9.47) = 9.47 minutes
Therefore, it would take approximately 9.47 minutes for the Officejet and Laserjet printers to copy the dissertation when working together.