Question

During a catered lunch, an average of 4 cups of tea are poured per minute. The lunch will last 2 hours. How many gallons of tea should the caterer bring if there are 16 cups in one gallon?

Answer 1

let's set up the conversion, starting with 4 cups per minute. since we want to know how many gallons they should bring for 1 lunch, the final units should be gallons/lunch

\[\frac{ 4~cups }{ minute }\frac{ 60~minutes }{ 1~hour }\frac{ 2~hours }{ 1~lunch }\frac{ 1~gallon }{ 16~cups }\]
since there are 60 minutes in one hour, we can multiply by (60 minutes/hr) to get the units in hours and cancel out minutes. similarly, since 1 lunch = 2 hours, we can multiply by 2 hours/lunch to get lunch in the "denominator". from there, since we have 4 cups, we can use the conversion factor 1 gallon/16 cups to cancel out the cups units and end up with gallons. notice how units cancel out.