Mastering Round Trip Distance, Speed, and Time Problems

Algebra 2 Grades High School 7:36 Video
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Lesson Description

Learn how to solve round trip distance, speed, and time problems using the formula distance = speed x time and a structured table approach. Ideal for Algebra 2 students.

Video Resource

Distance Speed Time Round Trip | Part 1

Kevinmathscience

Duration: 7:36
Watch on YouTube

Key Concepts

  • Distance, Speed, and Time Relationship (d = st)
  • Round Trip Problems: Distance is the same in both directions
  • Using Tables to Organize Information

Learning Objectives

  • Students will be able to apply the formula d = st to solve round trip problems.
  • Students will be able to create and use a table to organize information in round trip problems.
  • Students will be able to calculate distance, speed, or time given the other two variables in a round trip scenario.

Educator Instructions

  • Introduction (5 mins)
    Briefly review the basic distance, speed, and time relationship (d = st). Discuss how this applies to real-world situations. Introduce the concept of 'round trip' scenarios where the distance is the same in both directions.
  • Video Viewing and Note-Taking (10 mins)
    Play the video 'Distance Speed Time Round Trip | Part 1' by Kevinmathscience. Instruct students to take notes on the key concepts and the problem-solving approach demonstrated in the video, particularly focusing on how the table is used.
  • Example Problem 1: Dublin Trip (15 mins)
    Work through the first example from the video (Dublin trip) on the board, emphasizing the table setup, identifying knowns and unknowns, and applying the d = st formula. Encourage student participation by asking questions at each step.
  • Example Problem 2: Stephanie's Trip (15 mins)
    Work through the second example from the video (Stephanie's trip) on the board, again emphasizing the table setup, identifying knowns and unknowns, and applying the d = st formula. Encourage students to solve alongside and ask clarifying questions.
  • Practice Problems (15 mins)
    Provide students with similar round trip problems to solve independently or in pairs. Circulate to provide assistance and answer questions.
  • Wrap-up and Review (5 mins)
    Summarize the key concepts and problem-solving strategies discussed in the lesson. Address any remaining questions or confusion.

Interactive Exercises

  • Create Your Own Problem
    Ask students to create their own round trip problem, including the known values and what needs to be found. Have students swap their problems and solve.

Discussion Questions

  • In a round trip problem, what quantity remains constant between the trip there and the return trip?
  • How does organizing the information in a table help solve distance, speed, and time problems?

Skills Developed

  • Problem-solving
  • Algebraic manipulation
  • Data organization
  • Critical thinking

Multiple Choice Questions

Question 1:

In a round trip problem, which of the following is always the same for both legs of the trip (assuming the path is the same)?

Correct Answer: Distance

Question 2:

The formula d = st represents the relationship between distance (d), speed (s), and time (t). If s = 60 mph and t = 2 hours, what is d?

Correct Answer: 120 miles

Question 3:

If the distance from City A to City B is 300 miles, and a car travels from City A to City B and back, what is the total distance traveled?

Correct Answer: 600 miles

Question 4:

A plane flies to a city 500 miles away. On the return trip, it experiences a headwind, causing it to travel slower. Which factor is affected by the headwind?

Correct Answer: Both speed and time

Question 5:

Why is it useful to create a table when solving distance, speed, and time problems?

Correct Answer: It helps organize the given information.

Question 6:

A train travels to a destination and back. The trip there takes 5 hours, and the return trip takes 4 hours. If the average speed on the return trip is 80 mph, what is the distance to the destination?

Correct Answer: 320 miles

Question 7:

Stephanie drives to her friend's house and back. The trip to her friend's house takes 2 hours at 40 mph. What is the distance to her friend's house?

Correct Answer: 80 miles

Question 8:

Using the d = st formula, what is the formula to solve for speed?

Correct Answer: s = d/t

Question 9:

A car travels 150 miles to its destination and 150 miles back in 5 hours. What is the average speed?

Correct Answer: 60 mph

Question 10:

A cyclist completes a 24 mile round trip. On the way there, he rides at 8 mph, but on the return he rides 50% faster. What is his speed on the return?

Correct Answer: 16 mph

Fill in the Blank Questions

Question 1:

The formula that relates distance, speed, and time is distance = speed x _______.

Correct Answer: time

Question 2:

In a round trip problem, the _______ is the same for both the trip there and the return trip.

Correct Answer: distance

Question 3:

If a car travels 200 miles in 4 hours, its average speed is _______ mph.

Correct Answer: 50

Question 4:

If the distance is 100 miles and the speed is 25 mph, the time it takes to travel is _______ hours.

Correct Answer: 4

Question 5:

Organizing information in a _______ can make distance, speed, and time problems easier to solve.

Correct Answer: table

Question 6:

If a plane travels 600 miles to its destination and back, the total distance traveled is _______ miles.

Correct Answer: 1200

Question 7:

If a car travels at a speed of 55 miles per hour for 3 hours, its distance is _______ miles.

Correct Answer: 165

Question 8:

The average speed can be found by dividing the _______ by the time.

Correct Answer: distance

Question 9:

In the video, the presenter solved the problems by creating a _______ with columns for distance, speed, and time.

Correct Answer: table

Question 10:

A trip to a destination and the trip back is called a _______ trip.

Correct Answer: round

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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