Math problem set Grade 6 Careers & CTE

Cottonwood Pump Station Flow Log: Rates and Percents

A grade 6 careers math set where students use a pump operator's flow log to work with gallons-per-minute unit rates, a ratio, a percent full, and one MGD conversion.

Grade: Grade 6
Subject: Careers & CTE
Material: Math problem set
Time: 40 min
Prep: No prep
Materials: Calculator (optional)

Standards

6.RP.A.2 Common Core Math

Understand the concept of a unit rate a/b associated with a ratio a:b with b not equal to 0, and use rate language in the context of a ratio relationship.

How this material aligns: Problems 1 through 3 have students use the gallons-per-minute unit rate of each pump to find totals over time, the per-one rate reasoning this standard defines.

All materials for 6.RP.A.2 →

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: Problem 7 finds what percent of the tank is full and problem 8 converts using 694 gpm per MGD, the percent and unit-conversion work this standard targets.

All materials for 6.RP.A.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 use a gallons-per-minute rate to find totals moved over a set time.
Students will find a percent full and compare a pump rate to a station's rated capacity.

Vocabulary

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: gallons per minute, unit rate, ratio

Teacher overview

A pump station operator keeps a flow log, a record of how much water is moving each minute and how much has been pumped. This set uses one such log for a fictional station so that every problem builds on the same numbers. Students work with gallons-per-minute rates, a ratio, a percent, and one simple conversion. A common misconception this set targets is mixing up a rate with a total: a pump's 250 gallons per minute is a rate, and it only becomes a number of gallons after you multiply by the minutes it runs.

Cottonwood Pump Station Flow Log: Rates and Percents — Grade 6 Careers & CTE

Name: ____________________________ Date: ______________

Problems

Use this flow log from Cottonwood Pump Station, a fictional station run by the town of Junction Bluff. Pump A moves water at 250 gallons per minute (gpm). Pump B moves water at 300 gpm. The station's empty storage tank holds 90,000 gallons. Show every step.

Pump A runs at 250 gpm. How many gallons does Pump A move in 10 minutes?
How many gallons does Pump A move in one hour, which is 60 minutes?
Pump B runs at 300 gpm. In one hour, how many more gallons does Pump B move than Pump A?
Write the ratio of Pump A's rate to Pump B's rate, 250 to 300, in simplest form.
The operator runs Pump A and Pump B together. What is their combined rate in gallons per minute?
Running both pumps together, how many minutes will it take to move 33,000 gallons?
The empty tank holds 90,000 gallons. After both pumps move 33,000 gallons into it, what percent of the tank is full? Round to the nearest whole percent.
The whole station is rated at 1 million gallons per day, which equals 694 gpm. Is the two-pump combined rate above or below 694 gpm, and by how many gpm?

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: 2,500 gallons.
250 gpm x 10 minutes = 2,500 gallons.
Answer: 15,000 gallons.
250 gpm x 60 minutes = 15,000 gallons.
Answer: 3,000 gallons.
Pump B moves 300 gpm x 60 minutes = 18,000 gallons in an hour. Pump A moves 15,000 gallons. 18,000 - 15,000 = 3,000 gallons more.
Answer: 5 to 6.
250 to 300 both divide by 50: 250 / 50 = 5 and 300 / 50 = 6, so the ratio is 5 to 6.
Answer: 550 gpm.
250 gpm + 300 gpm = 550 gpm combined.
Answer: 60 minutes.
33,000 gallons / 550 gpm = 60 minutes.
Answer: 37 percent.
33,000 gallons / 90,000 gallons = 0.3667, which rounds to 37 percent.
Answer: 144 gpm below.
The combined rate is 550 gpm. 694 gpm - 550 gpm = 144 gpm, so the two pumps together run 144 gpm below the station's rated 694 gpm.

Differentiation

Support

Give these students a filled-in first row showing "250 gallons per minute times 10 minutes equals 2,500 gallons" as a model, and provide the reminder "rate times minutes equals gallons" at the top so they multiply before comparing. Allow a calculator for every problem.

Extension

Ask students to find how many total minutes it would take the two pumps together to fill the whole 90,000-gallon tank, and then to check their answer by converting that time into hours and minutes.

ELL supports

Provide a labeled picture of the two pumps feeding one tank, with each pump's rate marked, before problem 1. Pre-teach "gallons per minute," "unit rate," "flow rate," and "ratio," and allow work to be shown with numbers and the diagram rather than full sentences.