Math problem set Grade 6 Math

Juniper Flats Well Pump Rates and One-Step Equations

A grade 6 problem set on a fictional subdivision's well pump, using unit rate in gallons per minute and one-step equations to plan filling a storage tank.

Grade: Grade 6
Subject: Math
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 and 8 have students find and compare a pump's unit rate in gallons per minute from a total and a time, the associated-unit-rate concept this standard defines.

All materials for 6.RP.A.2 →

6.EE.B.7 Common Core Math

Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.

How this material aligns: Problems 2, 3, 7, and 10 ask students to write and solve equations of the form px equals q and x plus p equals q for the tank fill, exactly the one-step equations this standard names.

All materials for 6.EE.B.7 →

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 find a pump's unit rate in gallons per minute from a total and a time.
Students will write and solve one-step equations to plan filling a storage tank.

Vocabulary

Pump: A pump is a machine that adds energy to water to move it or push it uphill, doing the job gravity cannot do on its own. Water systems use many different kinds of pumps to move water from wells, through treatment, and out to customers.

Also: unit rate, equation, storage tank

Teacher overview

A well pump lifts water from underground into a storage tank that serves nearby homes. Knowing the pump's rate in gallons per minute lets an operator plan how long a fill will take. This problem set follows Juniper Flats, a fictional subdivision, and moves from unit rate to one-step equations. A common mistake to watch for is dividing the total by the wrong number when finding the rate; the rate is gallons divided by minutes, not minutes divided by gallons.

Juniper Flats Well Pump Rates and One-Step Equations — Grade 6 Math

Name: ____________________________ Date: ______________

Problems

Use these numbers for the whole set. In this fictional subdivision, the Juniper Flats well pump runs at a steady rate. In 20 minutes it pumps 900 gallons. The storage tank holds 5,400 gallons.

What is the pump's unit rate in gallons per minute?
Write and solve an equation to find how many minutes it takes to pump 5,400 gallons at that rate.
The tank already holds 900 gallons. Write and solve an equation of the form x plus 900 equals 5,400 to find how many more gallons are needed to fill it.
How many minutes does it take to pump those extra gallons from problem 3 at the pump's rate?
Change your answer from problem 2 into hours and minutes.
The pump runs for 30 minutes. How many gallons does it move in that time?
The pump must deliver 2,700 gallons for a fire drill. Write and solve an equation of the form 45 times x equals 2,700 to find the minutes needed.
A second, smaller pump moves 600 gallons in 20 minutes. What is its unit rate in gallons per minute, and which pump is faster?
Explain why knowing the pump's gallons-per-minute rate helps the operator plan the day.
The operator wants the empty tank filled in exactly 90 minutes. Write and solve an equation of the form 90 times r equals 5,400 to find the rate needed.

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: 45 gallons per minute. 900 gallons ÷ 20 minutes = 45 gallons per minute.
Answer: 120 minutes. The equation is 45 times x = 5,400, so x = 5,400 ÷ 45 = 120 minutes.
Answer: 4,500 gallons. The equation x + 900 = 5,400 gives x = 5,400 − 900 = 4,500 gallons.
Answer: 100 minutes. 4,500 gallons ÷ 45 gallons per minute = 100 minutes.
Answer: 2 hours. 120 minutes ÷ 60 = 2 hours and 0 minutes.
Answer: 1,350 gallons. 45 gallons per minute × 30 minutes = 1,350 gallons.
Answer: 60 minutes. The equation 45 times x = 2,700 gives x = 2,700 ÷ 45 = 60 minutes.
Answer: 30 gallons per minute; the first pump is faster. 600 ÷ 20 = 30 gallons per minute, and 45 is greater than 30.
Answer: The rate tells the operator how many gallons come each minute, so the operator can multiply or divide to know how long any fill will take before starting.
Answer: 60 gallons per minute. The equation 90 times r = 5,400 gives r = 5,400 ÷ 90 = 60 gallons per minute.

Differentiation

Support

Give students the pump rate (45 gallons per minute) already found so they can start at problem 2. Provide a two-step reminder card: "rate = gallons ÷ minutes" and "to undo times, divide." Allow a calculator for the division in problems 4, 7, and 10.

Extension

Ask students to figure out how long the first pump and the second pump would take, working together at the same time, to fill the 5,400-gallon tank from empty, and to explain how they combined the two rates.

ELL supports

Pre-teach "pump," "storage tank," "unit rate," and "equation" with a labeled drawing of a well, a pump, and a tank. Provide sentence frames for the equations: "45 times x = ___" and "x + 900 = ___." Allow students to label the drawing with their numbers as shown work.