Solving Work-Rate Problems: Teamwork Makes the Dream Work!

Algebra 2 Grades High School 22:59 Video
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Lesson Description

Learn how to solve 'working together' word problems using algebraic equations. This lesson breaks down the core concepts and provides strategies to tackle these problems with confidence.

Video Resource

Working Together Word Problem Equations

Kevinmathscience

Duration: 22:59
Watch on YouTube

Key Concepts

  • Work rate as a fraction of the job done per unit of time.
  • Setting up equations representing individuals' work rates and combined work rates.
  • Solving rational equations with one variable.
  • Understanding the concept of combined work being faster than individual work.

Learning Objectives

  • Students will be able to translate 'working together' word problems into algebraic equations.
  • Students will be able to solve rational equations to find the time it takes for individuals or groups to complete a task.
  • Students will be able to interpret the solutions of work-rate problems in the context of the original problem.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing basic concepts of rate, time, and work. Engage students with a real-life example of teamwork speeding up a task. Briefly introduce the concept of representing work rate as a fraction.
  • Video Explanation (15 mins)
    Play the Kevinmathscience video 'Working Together Word Problem Equations'. Pause at key points to emphasize the core concepts. Discuss the initial wall painting example and how the fraction of work done in one hour is crucial.
  • Example Problems (20 mins)
    Work through the bowling alley oiling example from the video step-by-step. Show how to translate the word problem into an equation. Focus on finding a common denominator and solving for the unknown variable. Present the second apple picking example to reinforce the concepts. Emphasize the logic behind combined work rate resulting in a faster completion time.
  • Different Question Type (15 mins)
    Present the attic cleaning example where the combined work time is given. Guide students to recognize the difference and how to adjust the equation accordingly. Reinforce that the 'together' portion is always on one side of the equal sign. Show them that the unknown could be on the left side of the equation instead of the right side.
  • Practice and Application (15 mins)
    Provide students with practice problems of varying difficulty levels. Encourage them to work in pairs or small groups. Circulate to provide support and address individual questions.
  • Wrap-up and Review (5 mins)
    Summarize the key steps in solving work-rate problems. Review the different types of problems presented. Assign homework for further practice.

Interactive Exercises

  • Group Problem Solving
    Divide students into groups and assign each group a different work-rate problem. Have them work together to solve the problem and present their solution to the class.
  • Online Worksheet
    Assign an online worksheet with a variety of work-rate problems. Use the results to identify areas where students need additional support.

Discussion Questions

  • Why is it important to express the work rate as a fraction of the job done in one unit of time?
  • How does the combined work rate compare to the individual work rates? Why?
  • What are some real-world scenarios where understanding work-rate problems would be useful?

Skills Developed

  • Translating word problems into algebraic equations.
  • Solving rational equations.
  • Critical thinking and problem-solving.
  • Collaboration and teamwork.

Multiple Choice Questions

Question 1:

What is the fundamental concept used to solve work-rate problems?

Correct Answer: Determining the fraction of work done per unit of time

Question 2:

If person A can complete a task in 5 hours, what fraction of the task can they complete in 1 hour?

Correct Answer: 1/5

Question 3:

What is the general form of the equation used to solve 'working together' problems, where A and B are individuals and T is their combined time?

Correct Answer: 1/A + 1/B = 1/T

Question 4:

Why is it important to find a common denominator when solving work-rate equations?

Correct Answer: To eliminate the fractions and solve the equation

Question 5:

Person X can paint a room in 3 hours, and Person Y can paint the same room in 6 hours. If they work together, will it take more or less than 3 hours?

Correct Answer: Less than 3 hours

Question 6:

Maria can type a 50-page document in 5 hours. Jose can type the same document in 4 hours. What fraction is represented by each person completing the document in one hour?

Correct Answer: Maria (1/5) Jose (1/4)

Question 7:

If two people work together, the amount of time to complete a job will be the time of the faster person alone.

Correct Answer: Less than

Question 8:

If you find that the combined work rate is 1/x, what does 'x' represent?

Correct Answer: The time it takes to complete the whole job together

Question 9:

When solving the equation, 1/x + 1/5 = 1/2, what is the first step?

Correct Answer: Find the lowest common denominator

Question 10:

Bob takes 4 hours to paint a wall. In a work-rate problem, this means in 1 hour, Bob can paint of the wall.

Correct Answer: 1/4

Fill in the Blank Questions

Question 1:

In a work-rate problem, the amount of work done per unit of time is represented as a ________.

Correct Answer: fraction

Question 2:

The equation 1/A + 1/B = 1/T is used to find the _________ time it takes for two people working together.

Correct Answer: combined

Question 3:

When solving work-rate equations with fractions, it is necessary to find a _________ _________ to eliminate the denominators.

Correct Answer: common denominator

Question 4:

If John can complete a job in 8 hours, his work rate is _________ of the job per hour.

Correct Answer: 1/8

Question 5:

In work-rate problems, if the equation is 1/x + 1/3 = 1/2, x represents the _________ it takes for one person to complete the job alone.

Correct Answer: time

Question 6:

Amy can complete a job in 12 hours. Her work rate can be expressed as _________.

Correct Answer: 1/12

Question 7:

If someone is working 30 minutes of an hour, this can be expressed as _________ of an hour.

Correct Answer: 1/2

Question 8:

In order to solve these problems, you need to multiply both sides by the _________.

Correct Answer: denominator

Question 9:

If you are working together, but also have to stop from time to time, this is not working _________.

Correct Answer: efficiently

Question 10:

The three blocks used to draw together individuals are the same as _________.

Correct Answer: adding

Educational Standards

A2.A.1:Represent and solve mathematical and real-world problems using nonlinear equations, systems of linear equations, and systems of linear inequalities; interpret the solutions in the original context. A2.A.1.3:Solve one-variable rational equations and check for extraneous solutions. A2.A.2.4:Solve rational equations with real roots.

Teaching Materials

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