Catch-Up Conundrums: Mastering Distance, Speed, and Time in Algebra 2

Algebra 2 Grades High School 14:07 Video
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Lesson Description

Learn to solve 'catch-up' distance, speed, and time problems using algebraic techniques. This lesson focuses on setting up equations and using the D = ST (Distance equals Speed times Time) formula to find unknown values.

Video Resource

Solve Distance Speed Time Algebra 2 | Overtake

Kevinmathscience

Duration: 14:07
Watch on YouTube

Key Concepts

  • Distance, Speed, and Time Relationship (D = ST)
  • Setting up Algebraic Equations from Word Problems
  • Solving for Unknown Variables

Learning Objectives

  • Students will be able to set up a table to organize information from distance, speed, and time word problems.
  • Students will be able to apply the formula D = ST to solve for unknown distances, speeds, or times.
  • Students will be able to solve catch-up problems where one object is trying to catch another.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the basic relationship between distance, speed, and time. Introduce the formula D = ST. Briefly discuss how units are important (miles vs kilometers, hours vs minutes).
  • Video Instruction (15 mins)
    Play the Kevinmathscience video: 'Solve Distance Speed Time Algebra 2 | Overtake'. Encourage students to take notes on the examples provided, focusing on the table method and the application of the D = ST formula.
  • Guided Practice (15 mins)
    Work through the first example from the video on the board, emphasizing each step. Explain how to translate the word problem into an algebraic equation. Highlight the importance of identifying which quantities are known and which are unknown. Then have students work in pairs to solve the second example problem from the video.
  • Independent Practice (10 mins)
    Provide students with a similar distance, speed, and time 'catch-up' problem to solve independently. Circulate the room to offer assistance and answer questions.
  • Wrap-up and Assessment (5 mins)
    Review the key concepts and address any remaining questions. Briefly introduce the quizzes that students will complete in the following section for assessment.

Interactive Exercises

  • Problem Swap
    Students create their own 'catch-up' distance, speed, and time problem. Then, they swap problems with a partner and solve each other's problems.

Discussion Questions

  • How does changing the units of speed (e.g., mph to km/h) affect the rest of the problem?
  • In what real-world scenarios might you use these distance, speed, and time calculations?
  • What are some common mistakes to avoid when setting up these types of problems?

Skills Developed

  • Algebraic Problem Solving
  • Translating Word Problems into Equations
  • Critical Thinking

Multiple Choice Questions

Question 1:

The formula that relates distance, speed, and time is:

Correct Answer: D = S * T

Question 2:

If a car travels at 60 mph for 2 hours, what is the distance covered?

Correct Answer: 120 miles

Question 3:

Two cars start from the same point. Car A travels at 40 mph and Car B travels at 50 mph in the same direction. How much faster is Car B traveling compared to Car A?

Correct Answer: 10 mph

Question 4:

What does 'mph' stand for?

Correct Answer: Miles per hour

Question 5:

In a 'catch-up' problem, when one person catches another, what is true about the distance they have traveled?

Correct Answer: The distance is always the same.

Question 6:

Person A leaves a location and travels 20 miles per hour. Person B leaves the same location one hour later, traveling 30 miles per hour. Assuming Person B is trying to catch Person A, after how many hours of travel will Person B catch Person A?

Correct Answer: 3 hours

Question 7:

Mary leaves a movie theater and travels towards a lake. Adam leaves 2 hours later, traveling at 65 miles per hour to catch up to Mary. If Adam travels for 3 hours before catching Mary, how long was Mary traveling in total?

Correct Answer: 5 hours

Question 8:

Totakan leaves an airport and travels to a recycling plant. Ming leaves 2 hours later, traveling at 75 kilometers per hour to catch up. Ming travels for 3 hours before catching Totakan. What is the distance they both traveled?

Correct Answer: 225 kilometers

Question 9:

If Prav leaves a science museum and Kayla leaves 3 hours later, with Kayla driving for 2 hours to catch up at 65 miles per hour, how far is Prav from the museum when Kayla catches up?

Correct Answer: 130 miles

Question 10:

What should you do first when tackling a distance, speed, and time 'catch-up' problem?

Correct Answer: Set up a table to organize the information.

Fill in the Blank Questions

Question 1:

The formula that relates distance (D), speed (S), and time (T) is D = S * ______.

Correct Answer: T

Question 2:

If you know the distance and the speed, you can calculate the time by dividing the ______ by the speed.

Correct Answer: distance

Question 3:

If a car travels at a constant speed, the longer the time, the greater the ______ covered.

Correct Answer: distance

Question 4:

When solving 'catch-up' problems, it's helpful to create a ______ to organize the information given.

Correct Answer: table

Question 5:

In catch-up problems, the distances traveled by both parties at the moment one catches up to the other are usually the ______.

Correct Answer: same

Question 6:

If Person A leaves a location traveling at a certain speed and Person B leaves later to catch up, it is important to account for the ______ difference when determining the total travel time.

Correct Answer: time

Question 7:

When Kayla drove at 65 miles per hour for 2 hours to catch up to Prav, the total distance Kayla drove was ______ miles.

Correct Answer: 130

Question 8:

In a scenario where two objects are traveling, their ______ may be different, but the calculations still use the same distance formula.

Correct Answer: speed

Question 9:

To find Mary's average speed after Adam catches up to her, one divides the ______ Mary traveled by the time Mary traveled.

Correct Answer: distance

Question 10:

If Totakan travels for 5 hours and Ming travels for 3 hours before Ming catches up to Totakan, we know Ming left ______ hours later.

Correct Answer: 2

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.2:Generate and evaluate equivalent algebraic expressions and equations using various strategies.

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