Chasing the Horizon: Mastering Opposite Direction Word Problems

Algebra 2 Grades High School 24:30 Video
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Lesson Description

Learn to solve distance, speed, and time problems involving objects moving in opposite directions. This lesson covers setting up equations, using tables, and applying the formula: Distance = Speed x Time.

Video Resource

Distance Speed Time Opposite Direction

Kevinmathscience

Duration: 24:30
Watch on YouTube

Key Concepts

  • Distance, Speed, and Time Relationship (D = ST)
  • Setting up equations based on word problem information
  • Using tables to organize information

Learning Objectives

  • Students will be able to translate word problems into algebraic equations.
  • Students will be able to solve for unknown variables (distance, speed, or time) when objects are moving in opposite directions.
  • Students will be able to use a table to organize the known and unknown values in a distance-speed-time problem.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the basic formula: Distance = Speed x Time. Briefly discuss how this formula applies when two objects are moving in opposite directions. Mention the different types of distance problems, such as catch-up and round trip, covered in earlier lessons.
  • Video Viewing (15 mins)
    Watch the provided YouTube video: 'Distance Speed Time Opposite Direction' by Kevinmathscience. Pay close attention to how the problems are set up and solved.
  • Guided Practice (20 mins)
    Work through example problems similar to those in the video. Emphasize the importance of creating a table to organize the given information (distance, speed, time) for each object. Show students how to translate the word problem into an equation, considering whether the total distance or a combination of distances is given.
  • Independent Practice (15 mins)
    Assign practice problems for students to solve individually. Circulate to provide assistance and answer questions.
  • Wrap-up (5 mins)
    Review key concepts and answer any remaining questions. Preview the upcoming topics.

Interactive Exercises

  • Problem Solving Challenge
    Present a complex word problem involving multiple steps and variables. Have students work in small groups to solve the problem. Each group presents their solution and explains their reasoning.
  • Online Simulation
    Use an online simulation tool where students can manipulate the speed and time of two objects moving in opposite directions and observe the resulting distance. This allows students to visualize the relationship between the variables.

Discussion Questions

  • How does the formula D = ST change when objects are traveling in opposite directions?
  • What strategies can you use to determine whether to add or subtract distances in a given problem?

Skills Developed

  • Algebraic problem-solving
  • Critical thinking
  • Organization and data representation

Multiple Choice Questions

Question 1:

Two cars start from the same point and travel in opposite directions. Car A travels at 60 mph and Car B travels at 70 mph. How far apart are they after 3 hours?

Correct Answer: 390 miles

Question 2:

A train leaves a station and travels east at 80 mph. Another train leaves the same station one hour later and travels west at 90 mph. How long after the second train leaves will they be 430 miles apart?

Correct Answer: 3 hours

Question 3:

Two cyclists start at the same location and travel in opposite directions. One cyclist travels at 12 mph and the other at 15 mph. After how many hours will they be 81 miles apart?

Correct Answer: 3 hours

Question 4:

A boat travels upstream at 10 mph and a raft travels downstream at 2 mph. If they both start at the same point, how far apart will they be after 4 hours?

Correct Answer: 48 miles

Question 5:

Sarah and John leave their house at the same time, traveling in opposite directions. Sarah drives at 55 mph and John drives at 65 mph. After how many hours will they be 360 miles apart?

Correct Answer: 3 hours

Question 6:

Two runners start at the same point on a track and run in opposite directions. One runs at 8 mph, and the other runs at 10 mph. After 1.5 hours, how far apart are they?

Correct Answer: 27 miles

Question 7:

A plane flies east at 500 mph, while another plane flies west at 450 mph from the same airport. How long will it take for them to be 2850 miles apart?

Correct Answer: 3 hours

Question 8:

A hiker walks north at 3 mph, and another hiker walks south at 2 mph from the same trailhead. What will be the distance separating them after 5 hours?

Correct Answer: 4

Question 9:

Two ships leave port at the same time, traveling in opposite directions. One ship travels at 18 knots, the other at 22 knots. How far apart are they after 6 hours?

Correct Answer: 240 nautical miles

Question 10:

If two cars start at the same location, one traveling north at 45 mph and the other traveling south at 55 mph, how many hours will it take for them to be 500 miles apart?

Correct Answer: 5 hours

Fill in the Blank Questions

Question 1:

The formula that relates distance, speed, and time is Distance = Speed x ________.

Correct Answer: Time

Question 2:

When objects move in opposite directions, their individual distances are typically _______ to find the total distance.

Correct Answer: added

Question 3:

If two trains travel in opposite directions, the sum of their distances equals the _______ distance separating them.

Correct Answer: total

Question 4:

If two cars start at the same place and drive away from each other, they are traveling in _______ directions.

Correct Answer: opposite

Question 5:

A ________ is helpful for organizing known and unknown values for distance, speed, and time.

Correct Answer: table

Question 6:

In distance problems, if one object leaves later, you must adjust the _________ for that object.

Correct Answer: time

Question 7:

If two people are walking away from each other, the speed is the _______ of their individual speeds.

Correct Answer: sum

Question 8:

If one car is traveling at 'x' mph and the second car travels 10 mph slower, then the speed of the second car is x _______ 10.

Correct Answer: - (minus)

Question 9:

If the total distance between two moving objects is given as 500 miles, this value helps formulate the _______.

Correct Answer: equation

Question 10:

Solving distance, speed, time problems involving opposite directions requires the application of ____________ equations.

Correct Answer: algebraic

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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