Math problem set Grade 10 Science

Ashford Reservoir Water Budget: Acre-Feet and Days of Supply

A grade 10 problem set at the fictional Ashford Reservoir, building a drought water budget in acre-feet and solving an equation for the days until a critical low level.

Grade: Grade 10
Subject: Science
Material: Math problem set
Time: 45 min
Prep: No prep
Materials: Calculator

Standards

HSA-CED.A.1 Common Core Math

Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

How this material aligns: In problems 4 and 5 students write a one-variable equation for reservoir storage over time and solve it for the number of days until the critical level is reached.

All materials for HSA-CED.A.1 →

HSN-Q.A.1 Common Core Math

Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.

How this material aligns: Students convert among MGD, gallons, acre-feet, and days across problems 1, 6, and 7, choosing consistent units so each water-budget quantity can be combined correctly.

All materials for HSN-Q.A.1 →

HS-ESS3-1 NGSS

Construct an explanation based on evidence for how the availability of natural resources, occurrence of natural hazards, and changes in climate have influenced human activity.

How this material aligns: Problems 5, 8, 9, and 10 construct an evidence-based explanation of how drought inflow and dwindling reservoir storage drove the town's conservation order and how much longer the reduced demand makes the supply last.

All materials for HS-ESS3-1 →

Download Word file

This material is in the public domain (CC0) and may be copied, edited, and shared freely, without attribution. Updated 2026-07-23.

Objectives

Students will convert a daily water demand from MGD into acre-feet per day.
Students will build a reservoir water budget and find the net daily drawdown.
Students will write and solve an equation for the days until a critical storage level.

Vocabulary

Water budget: A water budget is a way of tracking all the water coming into an area, like rain and snowmelt, against all the water leaving it, like evaporation and streamflow. Scientists use water budgets to see whether a watershed or aquifer is gaining or losing water over time.
Acre-foot: The amount of water it takes to cover one acre of land, about the size of a football field, one foot deep. Western states use acre-feet to measure large amounts of water.
Drawdown: Drawdown is how far the water level in a well drops when a pump pulls water out. The harder and longer you pump, the bigger the drawdown gets.

Also: reservoir storage, days of supply

Teacher overview

A reservoir's water budget compares what comes in against what goes out, and in a drought the difference decides how long the supply lasts. This set uses the fictional Ashford Reservoir to build that budget in acre-feet, then writes an equation for the storage over time and solves for the day the reservoir hits a critical low. A common misconception is dividing total storage by demand alone to get days of supply; that ignores the daily inflow, so students must subtract inflow from demand to find the true net drawdown before any timeline makes sense.

Ashford Reservoir Water Budget: Acre-Feet and Days of Supply — Grade 10 Science

Name: ____________________________ Date: ______________

Problems

Ashford Reservoir (a fictional reservoir) supplies a town that uses 3.0 MGD. Use these facts and conversions: 1 acre-foot = 325,851 gallons; 3.0 MGD = 3,000,000 gallons per day; the reservoir currently holds 4,000 acre-feet; the utility will not draw the reservoir below a critical level of 1,000 acre-feet; during the drought the reservoir gains 2.0 acre-feet of inflow per day.

Convert the town's demand of 3.0 MGD into acre-feet per day, using 3.0 MGD = 3,000,000 gallons per day and 1 acre-foot = 325,851 gallons. Round to the nearest hundredth.
Find the net daily drawdown in acre-feet per day, subtracting the 2.0 acre-feet of daily inflow from the demand in problem 1.
The reservoir holds 4,000 acre-feet and cannot be drawn below 1,000 acre-feet. How many acre-feet are available to use before reaching the critical level?
Write an equation for the storage S, in acre-feet, after t days, starting at 4,000 acre-feet and dropping at the net drawdown rate from problem 2.
Using your equation, solve for the number of days t until the storage reaches the 1,000 acre-foot critical level. Round to the nearest whole day.
Convert the number of days from problem 5 into months, using 30 days per month. Round to the nearest whole month.
A conservation order cuts demand to 2.0 MGD. Convert 2.0 MGD (2,000,000 gallons per day) into acre-feet per day. Round to the nearest hundredth.
With the reduced demand from problem 7 and the same 2.0 acre-feet of daily inflow, find the new net drawdown and then the new number of days until the reservoir reaches the 1,000 acre-foot critical level. Round to the nearest whole day.
Compare the days until the critical level before conservation (problem 5) and after (problem 8). By how many days did the conservation order extend the supply?
Explain, using your numbers, why cutting demand by one-third extended the supply by far more than one-third of the original days.

From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.

Answer Key

Answer: 9.21 acre-feet per day. 3,000,000 gallons per day divided by 325,851 gallons per acre-foot = 9.207, which rounds to 9.21 acre-feet per day.
Answer: 7.21 acre-feet per day. Net drawdown = 9.21 demand − 2.0 inflow = 7.21 acre-feet per day.
Answer: 3,000 acre-feet. 4,000 acre-feet held − 1,000 acre-foot critical level = 3,000 acre-feet available.
Answer: S = 4,000 − 7.21t. Storage starts at 4,000 acre-feet and falls by the net drawdown of 7.21 acre-feet each day t.
Answer: 416 days. Set 1,000 = 4,000 − 7.21t, so 7.21t = 3,000 and t = 3,000 divided by 7.21 = 416.1, about 416 days.
Answer: 14 months. 416 days divided by 30 days per month = 13.87, which rounds to 14 months.
Answer: 6.14 acre-feet per day. 2,000,000 gallons per day divided by 325,851 = 6.138, which rounds to 6.14 acre-feet per day.
Answer: 725 days. New net drawdown = 6.14 − 2.0 = 4.14 acre-feet per day, and 3,000 divided by 4.14 = 724.6, about 725 days.
Answer: 309 days. 725 days after conservation − 416 days before = 309 more days of supply.
Answer: The inflow stays fixed at 2.0 acre-feet per day, so cutting demand shrinks the net drawdown by more than one-third: it fell from 7.21 to 4.14 acre-feet per day. Because days of supply divide the available storage by that smaller drawdown, the timeline stretches much more than one-third.

Differentiation

Support

Provide a printed reference card with "1 acre-foot = 325,851 gallons" and the storage equation form S = start − rate x t. Work problem 1 with students and give them the subtraction set up for problem 2 before they continue.

Extension

Ask students to find the maximum steady demand, in MGD, at which the reservoir would never fall below the 1,000 acre-foot critical level, given the 2.0 acre-feet of daily inflow, and explain what that break-even demand represents for long-term planning.

ELL supports

Provide a simple diagram of the reservoir with arrows for inflow and demand and a marked critical level line. Pair "drawdown," "inflow," and "acre-foot" with short definitions, and allow students to show the equation with numbers rather than writing full sentences.