Math problem set Grade 6 Science

Oakspur Plant Detention Time: How Long Water Settles

A grade 6 science math set where students find a fictional basin's volume, then divide by flow to get detention time and check it against the 2-to-4-hour design range.

Grade: Grade 6
Subject: Science
Material: Math problem set
Time: 40 min
Prep: No prep
Materials: Calculator

Standards

6.RP.A.3 Common Core Math

Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations, including finding a percent of a quantity and converting measurement units.

How this material aligns: Problems 3, 4, and 6 use rate reasoning to divide a basin volume by a flow rate and convert the resulting detention time between hours and minutes.

All materials for 6.RP.A.3 →

6.NS.B.3 Common Core Math

Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

How this material aligns: Problems 1 and 2 require multiplying multi-digit values, including 16,000 by the decimal 7.48, and problem 3 divides multi-digit numbers to find detention time.

All materials for 6.NS.B.3 →

MS-ETS1-1 NGSS

Define the criteria and constraints of a design problem with sufficient precision to ensure a successful solution, taking into account relevant scientific principles and potential impacts on people and the natural environment that may limit possible solutions.

How this material aligns: Problems 5, 6, and 7 test the basin's computed detention time against the stated 2-to-4-hour design range as the flow constraint rises from 48,000 to 60,000 gallons per hour, the criteria-and-constraints definition this standard requires.

All materials for MS-ETS1-1 →

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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 find the volume of a rectangular basin in cubic feet and convert it to gallons.
Students will divide volume by flow to find detention time and convert it to minutes.
Students will explain how changing the flow changes the detention time.

Vocabulary

Detention time: Detention time is how long water stays inside a tank or basin before flowing out. Water must stay long enough for each treatment step, like settling or disinfecting, to finish its job.
Flow rate: Flow rate measures how much water moves past a point in a certain amount of time, like gallons per minute through a garden hose. Bigger pipes and stronger pushes give bigger flow rates.

Also: sedimentation basin, volume

Teacher overview

At a water plant, dirty water sits in a sedimentation basin so heavy bits can settle to the bottom. Detention time is how long the water stays in the basin, found by dividing the basin's volume by the flow rate. This set uses the fictional Oakspur Water Treatment Plant. A common mistake is thinking that a faster flow gives a longer detention time; in fact, dividing by a larger flow gives a shorter time, so watch the direction of that change in problems 6 and 7.

Oakspur Plant Detention Time: How Long Water Settles — Grade 6 Science

Name: ____________________________ Date: ______________

Problems

Suppose the Oakspur plant has one rectangular sedimentation basin. It is 50 feet long, 40 feet wide, and 8 feet deep. Water flows through it at 48,000 gallons per hour. Use these numbers for the problems.

Find the basin's volume in cubic feet. Volume equals length times width times depth.
Convert the volume to gallons. One cubic foot holds 7.48 gallons.
Detention time equals volume divided by flow. The basin holds 119,680 gallons and the flow is 48,000 gallons per hour. Find the detention time in hours. Round to the nearest tenth.
Convert your detention time from problem 3 into minutes. Round to the nearest whole minute.
Plants usually design a sedimentation basin for 2 to 4 hours of detention time. Is Oakspur's basin inside that range?
On a busy day the flow rises to 60,000 gallons per hour. Find the new detention time in hours, using the same 119,680-gallon volume. Round to the nearest tenth.
When the flow went up, did the detention time go up or down? Explain why, using the formula detention time equals volume divided by flow.
Explain why a longer detention time helps the basin remove more dirt from the water.

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: 16,000 cubic feet.
Volume equals length times width times depth. 50 x 40 x 8 = 16,000 cubic feet.
Answer: 119,680 gallons.
Multiply the cubic feet by 7.48. 16,000 x 7.48 = 119,680 gallons.
Answer: 2.5 hours.
Detention time equals volume divided by flow. 119,680 / 48,000 = 2.49, which rounds to about 2.5 hours.
Answer: 150 minutes.
Multiply hours by 60. 2.49 x 60 = 149.6, which rounds to about 150 minutes.
Answer: Yes.
The detention time of about 2.5 hours falls between 2 and 4 hours, so the basin is inside the usual design range.
Answer: 2.0 hours.
Use the same 119,680-gallon volume with the higher flow. 119,680 / 60,000 = 1.99, which rounds to about 2.0 hours.
Answer: The detention time went down.
In the formula, volume is divided by flow. A larger flow means dividing by a bigger number, so the detention time gets shorter when the flow rises.
Answer: More time lets more heavy bits settle to the bottom before the water leaves.
Accept any answer that connects a longer stay in the basin to more particles settling out of the water.

Differentiation

Support

Give students the volume formula and the 7.48 conversion on a printed card. Work problem 1 and problem 2 together as a class, then let students continue. Allow calculator use for the division in problems 3 and 6.

Extension

Ask students to find the flow rate, in gallons per hour, that would give an exact detention time of 4 hours in this basin, working backward from the 119,680-gallon volume. Have them explain what a very slow flow would mean for the plant on a low-use day.

ELL supports

Provide a labeled diagram of the basin showing length, width, and depth as three separate measurements. Give the sentence frame "Detention time equals ___ divided by ___" and allow students to show work with numbers and the diagram rather than sentences.