the office jet printer can copy maria's dissertation in 16min the laser jet printer can copy the same document in 8min if the two machines work together how long would they take to copy the dissertation
These problems are solved in the following way:
x / 16 + x / 8 = 1
Bringing these two fractions to the common denominator (which, in this case, is 16), we get the following:
x / 16 + 2x / 16= 1
3x / 16 = 1
Solving the above equation for x, we get the following:
x = 1 : 3/16 [reciprocal]
x = 16 / 3 = 5.3 min
and 5.3 min = [approximately] 5 minutes 20 seconds
To find out how long it would take for the two machines to copy the dissertation when working together, we need to calculate their combined efficiency.
Let's assume the office jet printer's copying rate is represented by O, and the laser jet printer's copying rate is represented by L. We are given that the office jet printer can copy Maria's dissertation in 16 minutes (O = 1/16) and the laser jet printer can do it in 8 minutes (L = 1/8).
When two machines work together, their combined copying rate is the sum of their individual rates. Therefore, their combined copying rate is O + L.
So, the combined copying rate for the office jet printer and the laser jet printer is (1/16) + (1/8) = 3/16.
To calculate the time it would take for them to copy the dissertation together, we can use the formula:
Time = 1 / Combined Rate.
Substituting in the combined rate we calculated, we get:
Time = 1 / (3/16) = 16/3 minutes.
Therefore, when the two machines work together, they would take approximately 5 and 1/3 minutes to copy Maria's dissertation.