Math problem set Grade 6 Engineering & Design

Pinebrook Garden Club Irrigation Pump Selection Problems

Eight problems where a fictional garden club compares two irrigation pumps' unit rates, solving one-step equations to find pumping time and check a time rule.

Grade: Grade 6
Subject: Engineering & Design
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 2 have students identify each pump's unit rate in gallons per minute and use it to find pumping time for the same 150-gallon job.

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 1, 2, 5, and 6 require writing and solving one-step equations of the form px = q, such as 3t = 150, to find pumping time from a known rate.

All materials for 6.EE.B.7 →

MS-ETS1-2 NGSS

Evaluate competing design solutions using a systematic process to determine how well they meet the criteria and constraints of the problem.

How this material aligns: Problems 3, 4, and 7 compare Pump A and Pump B on pumping time and price and judge each against the club's 45-minute session rule, and problem 8 tests a third pump rated at 7 gallons per minute against the spigot's 6-gallon-per-minute supply constraint, the systematic comparison of competing options against criteria this standard describes.

All materials for MS-ETS1-2 →

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This material is in the public domain (CC0) and may be copied, edited, and shared freely, without attribution. Updated 2026-07-16.

Objectives

Students will identify each pump's unit rate in gallons per minute and use it to compare pumping times.
Students will write and solve one-step equations of the form px = q to find how long a pump takes to deliver a given amount of water.
Students will check a pump's performance against a stated time constraint.

Vocabulary

Key words: unit rate, equation, constraint

Teacher overview

The Pinebrook Middle School garden club (a fictional club used for this problem set) is choosing an irrigation pump for its raised garden beds and is comparing two pump options by their unit rate in gallons per minute. This problem set uses each pump's rate to find pumping time through one-step equations, then checks the results against the club's own time rule. A common misconception in this set is solving an equation like 3t = 150 by subtracting 3 from 150 instead of dividing 150 by 3; watch for that error, since dividing by the rate is the only operation that isolates the pumping time.

Pinebrook Garden Club Irrigation Pump Selection Problems — Grade 6 Engineering & Design

Name: ____________________________ Date: ______________

Problems

All pump rates and prices in this problem set are fictional, chosen for this scenario. The garden's raised beds need 150 gallons of water per watering session.

Pump A pumps water at a rate of 3 gallons per minute. Write and solve the equation 3t = 150 to find how many minutes Pump A takes to deliver 150 gallons.
Pump B pumps water at a rate of 5 gallons per minute. Write and solve the equation 5t = 150 to find how many minutes Pump B takes to deliver the same 150 gallons.
How many fewer minutes does Pump B take than Pump A, based on problems 1 and 2?
Pump A costs $45 and Pump B costs $70. Find the price difference between the two pumps.
The garden club waters twice a week, for a weekly total of 300 gallons. Using Pump A's rate, write and solve an equation of the form 3t = 300 to find the total weekly pumping time.
Using Pump B's rate, write and solve an equation to find the total weekly pumping time needed for the same 300 gallons.
The garden club has a rule that no single watering session may run longer than 45 minutes. Using your answers to problems 1 and 2, does Pump A meet this rule? Does Pump B?
Challenge: the garden's outdoor spigot can supply water at a maximum rate of 6 gallons per minute. If a third pump were rated at 7 gallons per minute, could it actually deliver water at its full rated speed from this spigot? Explain your reasoning using the idea of a constraint.

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: 50 minutes. 3t = 150, so t equals 150 divided by 3, which is 50 minutes.
Answer: 30 minutes. 5t = 150, so t equals 150 divided by 5, which is 30 minutes.
Answer: 20 minutes. 50 minus 30 equals 20 fewer minutes for Pump B.
Answer: $25. $70 minus $45 equals $25.
Answer: 100 minutes. 3t = 300, so t equals 300 divided by 3, which is 100 minutes.
Answer: 60 minutes. 5t = 300, so t equals 300 divided by 5, which is 60 minutes.
Answer: Pump A does not meet the rule; Pump B does. Pump A's 50 minutes (problem 1) is longer than the 45-minute limit, while Pump B's 30 minutes (problem 2) is under the limit.
Answer: No, it could not. A pump can only move as much water as its water source supplies, so if the spigot supplies water at a maximum of 6 gallons per minute, a pump rated for 7 gallons per minute is limited to the spigot's 6-gallon-per-minute rate; the spigot becomes the binding constraint regardless of the pump's own rating.

Differentiation

Support

Provide a filled-in example equation, 4t = 200, solved step by step (t equals 200 divided by 4, which is 50), as a model before students solve problems 1, 2, 5, and 6 on their own, and allow a calculator for every division step.

Extension

Ask students to find a pump rate, in whole gallons per minute, that would deliver 150 gallons in exactly 25 minutes, using the equation rt = 150 and solving for r.

ELL supports

Pre-teach "rate," "equation," and "constraint" using a simple diagram of a hose filling a bucket, with an arrow labeled "gallons per minute" pointing into the bucket. Allow students to show equation work as numbers on a simple two-line solution, the equation and then the answer, rather than full sentences.

Extensions

Have students research, using only teacher-provided rate cards, a third real garden-hose flow rate and calculate how long it would take to deliver the same 150 gallons, adding it to a class comparison table of pump and hose options.