A printer takes 50 minutes to print a total of 1200 identical black-and-white posters and 500 identical coloured posters. The same printer takes 1 hour to print 2400 such black-and-white posters. How many such coloured posters can the same printer print in 1 hour?
Do you usually set up two equations in two unknowns for this ? Or work at it with proportional reasoning? Both methods are valid : )
(1200/2400) * 1h = 0.5h = 30 min. to print 1200 black-and -white posters,
50 - 30 = 20 min. to print 500 colored posters,
(60min/20min) * 500 = 1500 colored posters in 1 hour.
To find out how many colored posters the printer can print in 1 hour, we need to determine the printing rate of the printer for colored posters.
We know that the printer takes 50 minutes to print a total of 1200 black-and-white posters and 500 colored posters. Let's first calculate the printing rate per minute for these two types of posters.
For black-and-white posters:
Printing rate per minute = Total posters / Time taken
Printing rate per minute = 1200 black-and-white posters / 50 minutes
Printing rate per minute = 24 black-and-white posters per minute
For colored posters:
Printing rate per minute = Total posters / Time taken
Printing rate per minute = 500 colored posters / 50 minutes
Printing rate per minute = 10 colored posters per minute
Now we need to determine the printing rate per hour for black-and-white posters.
Printing rate per hour = Printing rate per minute * 60 (minutes in an hour)
Printing rate per hour = 24 black-and-white posters per minute * 60 minutes
Printing rate per hour = 1440 black-and-white posters per hour
Since it is given that the printer takes 1 hour to print 2400 black-and-white posters, we can calculate the printing rate per hour for black-and-white posters as follows:
Printing rate per hour = Total posters / Time taken
Printing rate per hour = 2400 black-and-white posters / 1 hour
Printing rate per hour = 2400 black-and-white posters per hour
Now, we can calculate the printing rate per hour for colored posters using the above information. Since both black-and-white and colored posters are printed by the same printer, we can assume that the printing rate per hour for colored posters will be the same as for black-and-white posters.
Printing rate per hour for colored posters = Printing rate per hour for black-and-white posters
Printing rate per hour for colored posters = 2400 colored posters per hour
Therefore, the same printer can print 2400 colored posters in 1 hour.