Unit 6, Lesson 17
Two Related Quantities, Part 2
Grade 6
17.2
Activity
Diego, Elena, and Andre joined different teams for a robotics competition. Each team programmed a robot to travel at a constant rate.
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Complete each table to show how far each team’s robot traveled during the competition.
Diego's Teamtime (minutes) distance traveled (meters) 1 1 2 6 4 5 Elena's Teamtime (minutes) distance traveled (meters) 1 1 2 4 11 5 Andre's Teamtime (minutes) distance traveled (meters) 1 1 2 4 5 17.5 -
Graph points to show the progress of each robot. Use a different color or symbol for each robot.
A blank coordinate grid with the origin labeled "O". The horizontal axis is labeled "time, in minutes" and the numbers 0 through 5, in increments of zero point 5, are indicated. The vertical axis is labeled "distance traveled, in miles" and the numbers 0 through 20 are indicated. -
Let’s say that represents the distance a robot traveled in meters and represents the time in minutes.
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Explain why relates the distance and time that Diego’s robot traveled.
- In this equation, which variable is independent and which one is dependent? Record your answer in the table. Be prepared to explain how you know.
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Complete the table with equations that can relate distance and time for the other two robots. Make sure that in each equation, the independent and dependent variables are as shown. Be prepared to explain your reasoning.
equation independent variable dependent variable Diego's team Elena's team time distance Andre's team distance time
Student Lesson Summary
Equations are very useful for solving problems that involve constant speed. Here is an example.
A boat travels at a constant speed of 25 miles per hour.
- How far can the boat travel in 3.25 hours?
- How long does it take for the boat to travel 60 miles?
We can write equations to help us answer questions like these.
Let's use to represent the time in hours and to represent the distance in miles that the boat travels.
When we know the time and want to find the distance, we can write:
In this equation, if changes, is affected by the change, so is the independent variable and is the dependent variable.
This equation can help us find when we have any value of . In hours, the boat can travel or 81.25 miles.
When we know the distance and want to find the time, we can write: In this equation, if changes, is affected by the change, so is the independent variable and is the dependent variable.
This equation can help us find for any value of . To travel 60 miles, it will take or hours.
We can also graph the two equations we wrote to get a picture of the relationship between the two quantities. By convention, the independent variable is represented on the horizontal axis.
A graph of 10 points plotted in the coordinate plane with the origin labeled "O". The horizontal t axis is labeled "time in hours". The numbers 0 through 10, in increments of 2, are indicated, and there are vertical gridlines midway between. The vertical axis is labeled "distance traveled in miles". The numbers 0 through 250, in increments of 25, are indicated, and there are horizontal gridlines midway between. The data are as follows: 1 comma 25. 2 comma 50. 3 comma 75. 4 comma 100. 5 comma 125. 6 comma 150. 7 comma 175. 8 comma 200. 9 comma 225. 10 comma 250.
Problems about constant speed can also be solved using other strategies, such as by making a table of equivalent ratios.
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