the officejet printer can copy maria'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?
rate1= 1/18
rate2=1/22
combined reate= rate1+rate2=40/18*22
combined rate= 1/9.9 min
so,9.9 min
LEt me show you another neat way.
In in 22*18 min, one machine can do 18, the other 22.
so rate= (18+22)/22*18
dissertations= rate*time
time= 1dissertation/rate= 22*18/40=9.9min
To determine how long it would take for the two printers to copy the dissertation if they work together, we need to find the "combined rate" at which they can copy the document. We can calculate this by finding the "copying speed" of each printer (expressed as "pages per minute") and then adding them together.
Let's denote the copying speed of the OfficeJet printer as "O" (pages per minute) and the copying speed of the LaserJet printer as "L" (pages per minute).
We have been given the following information:
- OfficeJet copying speed (O) = 1 copy per 18 minutes
- LaserJet copying speed (L) = 1 copy per 22 minutes
To find the combined rate, we add the copying speeds together:
Combined rate (O + L) = (1/18) + (1/22) copies per minute
Now, to find the time it takes to copy the whole dissertation, we invert the combined rate (to convert it to time per copy):
Time to copy dissertation = 1 / (O + L) minutes per copy
By plugging in the respective values, we can calculate the answer:
Time to copy dissertation = 1 / ((1/18) + (1/22))
Simplifying this expression will give us the final answer.