Math problem set Grade 12 Science

Highmarsh Reservoir Water Budget and Days of Supply

A grade 12 science problem set on a fictional reservoir: students move between acre-feet, gallons, and MGD to find net drawdown and how many days of supply remain.

Grade: Grade 12
Subject: Science
Material: Math problem set
Time: 45 min
Prep: No prep
Materials: Calculator

Standards

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 carry units through the acre-foot, gallon, and MGD conversions in problems 1 through 9, the multi-step dimensional analysis this standard names when sizing a water supply.

All materials for HSN-Q.A.1 →

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: Problems 4, 6, and 7 build and use the equation days of supply = usable storage / net loss rate to answer questions about how long the reservoir lasts.

All materials for HSA-CED.A.1 →

HS-ESS3-3 NGSS

Create a computational simulation to illustrate the relationships among the management of natural resources, the sustainability of human populations, and biodiversity.

How this material aligns: Problems 3 through 10 build a simplified reservoir budget of storage, inflow, demand, drought, and conservation to test how many days of supply remain, the resource-management calculation this standard permits.

All materials for HS-ESS3-3 →

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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 reservoir storage between acre-feet and gallons.
Students will calculate net drawdown from inflow and demand and express it in MGD.
Students will calculate days of supply from usable storage and a net loss rate.

Vocabulary

Reservoir: A human-made lake, usually created by a dam, that stores water for later. Reservoirs supply cities and farms and help control floods.
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.

Also: net drawdown, days of supply, reserve

Teacher overview

A reservoir's storage rises with inflow and falls with demand, and what remains is the water the town has on hand. This set uses the fictional town of Highmarsh and its reservoir to move between the units planners actually use, acre-feet for storage and million gallons per day for flow, and to work out how many days of supply remain under normal use and during a drought. The problems build in sequence, so a value found early is reused later.

A common misconception is to compare storage in acre-feet directly with demand in MGD without converting. Storage and flow are different kinds of quantities, and the conversion to a common unit, gallons, must come first. Problem 1 sets up that conversion so the later comparisons are valid.

Highmarsh Reservoir Water Budget and Days of Supply — Grade 12 Science

Name: ____________________________ Date: ______________

Problems

The town of Highmarsh (a fictional town used for this problem set) draws its water from Highmarsh Reservoir, which holds 4,000 acre-feet of usable storage. The town's population of 30,000 people uses 100 gallons per person per day. In summer the watershed delivers an average inflow of 2.0 MGD. Use these conversions for every problem.

1 acre-foot = 325,851 gallons
1 MGD = 1,000,000 gallons per day
Days of supply = usable storage (gallons) / net loss rate (gallons per day)

Convert the reservoir's usable storage of 4,000 acre-feet to gallons.
Calculate the town's total daily demand in gallons per day, then state it in MGD, using 30,000 people at 100 gallons per person per day.
During summer, calculate the net drawdown in MGD: the demand from problem 2 minus the inflow of 2.0 MGD.
If summer inflow and demand held steady, how many days would the usable storage from problem 1 last at the net drawdown rate from problem 3? Round to the nearest whole day.
Convert your days-of-supply answer from problem 4 to years, using 365 days per year. Round to the nearest tenth.
A drought cuts inflow to 0.5 MGD while demand stays at 3.0 MGD. Calculate the new net drawdown, then the new days of supply from the full usable storage. Round to the nearest whole day.
The town sets a rule to keep a reserve of 180 days of supply at the drought net-loss rate from problem 6. How many gallons must stay in reserve?
How many gallons of usable storage can be drawn down before hitting the reserve from problem 7?
Convert the drawdown allowance from problem 8 to acre-feet, using 1 acre-foot = 325,851 gallons. Round to the nearest whole acre-foot.
Suppose conservation lowers per-person use from 100 to 80 gallons per day. Calculate the new summer demand in MGD, then explain how that changes the drought net drawdown from problem 6.

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: 1,303,404,000 gallons.
4,000 acre-feet x 325,851 gallons per acre-foot = 1,303,404,000 gallons.
Answer: 3.0 MGD.
30,000 people x 100 gallons per person per day = 3,000,000 gallons per day, which is 3.0 MGD.
Answer: 1.0 MGD.
Net drawdown = demand - inflow = 3.0 MGD - 2.0 MGD = 1.0 MGD, a net loss of 1,000,000 gallons per day.
Answer: 1,303 days.
Days of supply = 1,303,404,000 gallons / 1,000,000 gallons per day = 1,303.4, which rounds to 1,303 days.
Answer: 3.6 years.
1,303.4 days / 365 days per year = 3.57, which rounds to 3.6 years.
Answer: 521 days.
New net drawdown = 3.0 MGD - 0.5 MGD = 2.5 MGD, or 2,500,000 gallons per day. Days of supply = 1,303,404,000 / 2,500,000 = 521.4, which rounds to 521 days.
Answer: 450,000,000 gallons.
Reserve = 180 days x 2,500,000 gallons per day = 450,000,000 gallons held back.
Answer: 853,404,000 gallons.
Drawdown allowance = usable storage - reserve = 1,303,404,000 - 450,000,000 = 853,404,000 gallons.
Answer: 2,619 acre-feet.
853,404,000 gallons / 325,851 gallons per acre-foot = 2,619.0, which rounds to 2,619 acre-feet.
Answer: 2.4 MGD.
New demand = 30,000 people x 80 gallons per person per day = 2,400,000 gallons per day, or 2.4 MGD. During the drought the net drawdown would fall from 2.5 MGD to 2.4 - 0.5 = 1.9 MGD, so the storage would last longer.

Differentiation

Support

Provide the three conversions on a reference card and complete problem 1 and problem 2 together. Give students a labeled place to write each intermediate value (storage in gallons, demand in MGD, net loss in gallons per day) so the later problems have their inputs ready.

Extension

Ask students to find the demand, in MGD, at which the drought net drawdown of problem 6 would give exactly 365 days of supply from the full usable storage, then state what per-person use that demand implies for 30,000 people.

ELL supports

Pre-teach "storage," "inflow," "demand," "drawdown," and "reserve" with a picture of a reservoir with an arrow in (inflow) and an arrow out (demand). Allow students to show problem 10 as a labeled calculation rather than full sentences.

Extensions

Have students look up the storage of a real nearby reservoir in acre-feet and its service population, then estimate a rough days-of-supply figure using this set's method. Comparing a real reservoir with Highmarsh turns the exercise into a question about their own supply.