An industrial printer produces 240 pages in 3 minutes when operating at full capacity. At this same rate, how many pages will the printer produce in 7.5 hours?
For rate and unit-conversion problems, first convert the given information into a clear unit rate (like pages per minute), then convert all other time or distance units to match that rate. Once units match, multiply the rate by the total time or quantity, checking units at each step to avoid common mistakes like forgetting to convert hours to minutes or using the wrong total time.
Hints
Find a unit rate first
You know the printer does 240 pages in 3 minutes. How can you find out how many pages it prints in 1 minute?
Match the time units
Your rate should be in pages per minute. How many minutes are in 7.5 hours? Remember to multiply by 60.
Combine rate and time
Once you know how many pages per minute the printer makes and how many minutes it runs, what operation will give you the total number of pages?
Desmos Guide
Calculate the total pages with one expression
In Desmos, type 240/3 * (7.5*60) and look at the numerical result. That value is the total number of pages the printer will produce in 7.5 hours at the given rate.
Step-by-step Explanation
Find the printer’s rate in pages per minute
The printer produces 240 pages in 3 minutes. To find pages per minute, divide the number of pages by the number of minutes:
So the printer prints 80 pages each minute.
Convert 7.5 hours to minutes
The rate we found is in pages per minute, so we need the total printing time in minutes.
There are 60 minutes in 1 hour, so:
So 7.5 hours is 450 minutes.
Multiply rate by total time to get total pages
Now multiply the rate (pages per minute) by the total number of minutes:
So the printer will produce 36,000 pages in 7.5 hours, which corresponds to choice C) 36,000.