Math CentralQuandaries & Queries


Question from Abigail, a student:

The City of Ames water treatment plant treats 7 million gallons of water per day on average to meet water demands. Hypothetically, if water is withdrawn from a groundwater system with an area of 51.6 square miles (approximate area of Ames and surrounding area), what is the depth of water in inches that would have to be added to the groundwater system annually to replace the water that is withdrawn by the city?

Hi Abigail,

My first question on seeing this problem was what units do I use. I decided to use feet and then convert the depth in feet to inches.

There are 5280 feet in a mile so 51.6 square miles times a depth of $d$ feet is $5280^2 \times 51.6 \times d$ cubic feet.

Type 1 gallon in cubic feet into Google to obtain the number of cubic feet in a gallon and then multiply by 7 million to obtain the average daily water usage in cubic feet. What is the overlade yearly water usage in cubic feet? Solve for $d.$


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