Math problem set Grade 7 Science

Graymoor's Sedimentation Basin: Volume and Detention Time

A grade 7 science problem set on a fictional plant's settling basin: students find its volume in gallons, its detention time, and the percent of turbidity removed.

Grade: Grade 7
Subject: Science
Material: Math problem set
Time: 45 min
Prep: No prep
Materials: Calculator

Standards

7.RP.A.3 Common Core Math

Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

How this material aligns: Problem 5 is a multistep percent problem computing the percent of turbidity a settling basin removes between its inlet and outlet, the percent reasoning this standard develops.

All materials for 7.RP.A.3 →

7.EE.B.4 Common Core Math

Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

How this material aligns: Problem 8 has students construct and solve the equation volume divided by flow equals three hours to find the maximum flow that keeps the target detention time, exactly this standard's work.

All materials for 7.EE.B.4 →

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: The set frames the basin around a detention-time criterion of at least three hours and a flow constraint, the precise definition of criteria and constraints this standard requires of a design problem.

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 calculate a rectangular basin's volume in cubic feet and convert it to gallons.
Students will use detention time equals volume divided by flow and find the percent of turbidity removed.

Vocabulary

Sedimentation: Sedimentation is the step where water sits almost still in a big basin so the heavy clumps of dirt can sink to the bottom. The cleaner water on top then moves on to the filters.
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.
Turbidity: Turbidity is a measure of how cloudy or murky water looks because of tiny particles floating in it. Clear water has low turbidity, and muddy water has high turbidity.

Also: basin

Teacher overview

In a sedimentation basin, water slows down so that heavy particles have time to settle to the bottom before the water moves on to the filters. Operators care about detention time, which is how long the average drop of water stays in the basin, found by dividing the basin's volume by the flow through it. This set follows a fictional plant, the Graymoor Water Treatment Plant, through those calculations. A common misconception this set corrects is dividing before converting units; the volume must be changed from cubic feet to gallons before it is divided by a flow measured in gallons per hour.

Graymoor's Sedimentation Basin: Volume and Detention Time — Grade 7 Science

Name: ____________________________ Date: ______________

Problems

The Graymoor Water Treatment Plant is fictional. Its sedimentation basin is a rectangular tank 60 feet long, 20 feet wide, and 12 feet deep. Use these facts: volume in cubic feet equals length times width times depth; one cubic foot holds 7.48 gallons; detention time equals volume in gallons divided by flow in gallons per hour.

What is the basin's volume in cubic feet?
Convert the volume from problem 1 to gallons.
The plant runs 30,000 gallons per hour through the basin. What is the detention time in hours? Round to the nearest tenth.
Sedimentation basins are usually designed for 2 to 4 hours of detention. Is the detention time from problem 3 inside that range?
Water enters the basin at 20 NTU of turbidity and leaves at 3 NTU. What percent of the turbidity does the basin remove?
During busy hours the flow rises to 40,000 gallons per hour. What is the new detention time, to the nearest tenth of an hour? Is it still inside the 2-to-4-hour range?
Explain why a higher flow gives a shorter detention time, and why a shorter detention time can lower how much the basin settles out.
The plant wants the detention time to stay at least 3 hours. Using volume divided by flow equals 3, find the largest flow, in gallons per hour, that meets this goal.

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: 14,400 cubic feet.
60 times 20 times 12 = 14,400 cubic feet.
Answer: 107,712 gallons.
14,400 times 7.48 = 107,712 gallons.
Answer: 3.6 hours.
107,712 divided by 30,000 = 3.59 hours, which rounds to 3.6 hours.
Answer: Yes, it is inside the range.
3.6 hours is between 2 and 4 hours, so the basin meets the usual design range.
Answer: 85%.
(20 − 3) divided by 20 times 100 = 17 divided by 20 times 100 = 85 percent removed.
Answer: 2.7 hours.
107,712 divided by 40,000 = 2.69 hours, which rounds to 2.7 hours, still between 2 and 4 hours.
Answer: Faster water spends less time in the basin.
When the flow rises, each drop passes through the basin more quickly, so heavy particles have less time to settle, which can leave more turbidity in the water leaving the basin.
Answer: 35,904 gallons per hour.
Volume divided by flow equals 3, so flow equals 107,712 divided by 3 = 35,904 gallons per hour is the largest flow that keeps a 3-hour detention time.

Differentiation

Support

Provide the three formulas on a reference card and complete problems 1 and 2 together so students carry the correct gallon figure into the later problems. Allow reuse of the 107,712 gallons from problem 2 throughout.

Extension

Ask students to redesign the basin so it holds a 4-hour detention time at 30,000 gallons per hour by changing only the depth, and to show what new depth is required.

ELL supports

Pre-teach "sedimentation," "detention time," and "turbidity" with a labeled side-view diagram of a basin showing water entering, particles settling, and clearer water leaving. Provide a units reminder card that cubic feet times 7.48 gives gallons.