The OfficeJet printer can copy Maria's dissertation in 18 min. The LaserJet printer can copy the same documents in 14 min. If the two machines work together, how long would they take to copy the dissertation?
Let that time be called T.
1/T = 1/18 + 1/14
1/T = 0.1270
T = 7.88 hours
That is more than half the time of the LaserJet alone.
The reason for the odd number is that you have to add have to the rates of doing the job. You don't average the times and divide by 2.
To find out how long it would take for the two printers to copy the dissertation together, we need to determine their combined copying rate.
We can start by calculating the copying rates for each printer. The OfficeJet printer copies the dissertation in 18 minutes, so its copying rate would be 1/18 dissertations per minute. Similarly, the LaserJet printer copies the same document in 14 minutes, so its copying rate would be 1/14 dissertations per minute.
To find the combined copying rate, we can add the individual copying rates together. So, the combined copying rate of the two printers would be 1/18 + 1/14 dissertations per minute.
To simplify the calculation, we need to find the least common denominator (LCD) of 18 and 14, which is 252. We can then rewrite the individual copying rates with the LCD as the common denominator: 14/252 + 18/252 dissertations per minute.
Adding the fractions together, we get 32/252 dissertations per minute.
To determine how long it would take for the two printers to copy the dissertation together, we can calculate the reciprocal of the combined copying rate. Reciprocating the fraction (32/252), we get 252/32 minutes per dissertation.
Simplifying this fraction, we find that it would take 7.875 minutes for the two printers to copy the dissertation together.
Therefore, the OfficeJet and LaserJet printers would take approximately 7.875 minutes to copy Maria's dissertation if they work together.