A packaging machine fills 15 jars of jam in 6 minutes. At this rate, how many jars can the machine fill in 54 minutes?
For constant-rate word problems, quickly convert the given information into a unit rate (such as jars per minute) or a simple proportion. Check how many times the original time interval fits into the new time (here ), then multiply the original quantity by that factor. Always track units (jars, minutes) as you work, and use mental math tricks like breaking numbers into tens and ones to avoid multiplication errors under time pressure.
Hints
Think in terms of rate
First, find how many jars the machine fills in 1 minute. Use the information that it fills 15 jars in 6 minutes.
Use a proportion or unit rate
You can either set up a proportion or compute jars per minute and then multiply by 54. Both methods should give the same result.
Multiply carefully
Once you know how many jars are filled in 1 minute, multiply that number by 54. Check your multiplication by breaking 54 into 50 and 4 if it helps.
Desmos Guide
Compute the scaled amount directly
In Desmos, type 15/6*54 or 15*(54/6) into the expression line. Look at the numeric output Desmos gives; that value is the number of jars the machine fills in 54 minutes at the given rate.
Step-by-step Explanation
Find the rate in jars per minute
We are told the machine fills 15 jars in 6 minutes.
Compute the rate (jars per minute):
This means every 1 minute, the machine fills jars.
Scale the rate up to 54 minutes
Now use the constant rate to find how many jars are filled in 54 minutes.
Multiply the rate by 54:
You can calculate this as .
State the total number of jars
From the calculation above:
So, in 54 minutes, the machine can fill 135 jars of jam.