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
If each was given half of the dissertation, wouldn't it be 19 minutes?
Wouln't it have to be a shorter timeframe since they are both working together? and one of them does it in 18 mins ..
To find out how long it would take for the two printers to copy the dissertation together, we need to calculate the combined rate at which they can copy.
Let's start by calculating the rate at which each printer can copy per minute:
Officejet printer: 1 dissertation / 18 min = 1/18 dissertations per minute
Laserjet printer: 1 dissertation / 20 min = 1/20 dissertations per minute
Now, to find the combined rate, we add the rates of the two printers:
Combined rate = 1/18 dissertations per minute + 1/20 dissertations per minute
We need to find a common denominator to add these fractions. The least common multiple (LCM) of 18 and 20 is 180.
So, the combined rate is:
= (1/18) * (20/20) + (1/20) * (18/18)
= 20/360 + 18/360
= 38/360 dissertations per minute
Now, to calculate the time it would take for the two printers to copy the dissertation together, we divide 1 dissertation by the combined rate:
Time = 1 dissertation / (38/360 dissertations per minute)
= 360/38 minutes
Simplifying the fraction, we get:
= 9.474 minutes (rounded to three decimal places)
Therefore, if the two printers work together, it would take approximately 9.474 minutes to copy the dissertation.