A Critical Look at Proportional Relationships

Examples, videos, and solutions to help Grade 8 students learn how to work with proportional relationships in terms of average speed and constant speed in order to write a linear equation in two variables.

New York State Common Core Math Grade 8, Module 4, Lesson 10

Worksheets for Grade 8

Lesson 10 Student Outcomes

• Students work with proportional relationships in terms of average speed and constant speed in order to write a linear equation in two variables.
• Students use linear equations in two variables to answer questions about distance and time.

Lesson 10 Summary

• Average speed is found by taking the total distance traveled in a given time interval, divided by the time interval.
• If we assume the same average speed over any time interval, then we have constant speed, which can then be used to express a linear equation in two variables relating distance and time.

NYS Math Module 4 Grade 8 Lesson 10 Examples & Exercises

Example 1
Paul walks miles in minutes. How many miles can Paul walk in minutes?

Example 2
Alexxa walked from the Grand Central Station on 42nd street to the Penn Station on 7th avenue. The total distance traveled was 1.1 miles. It took Alexxa 25 minutes to make the walk. How many miles did she walk in the first 10 minutes?

Exercises 1–3
1. Wesley walks at a constant speed from his house to school 1.5 miles away. It took him 25 minutes to get to school.
a. What fraction represents his constant speed, C?
b. You want to know how many miles he has walked after 15 minutes. Let y represent the distance he traveled after 15 minutes of walking at the given constant speed. Write a fraction that represents the constant speed, C in terms of y.
c. Write the fractions from parts (a) and (b) as a proportion and solve to find out many miles Wesley walked after 15 minutes.
d. Let y be the distance in miles that Wesley traveled after x minutes. Write a linear equation in two variables that represents how many miles Wesley walked after x minutes.

2. Stefanie drove at a constant speed from her apartment to her friend’s house 20 miles away. It took her 45 minutes to reach her destination.
a. What fraction represents her constant speed, C?
b. What fraction represents constant speed, c, if it takes her x number of minutes to get half-way to her friend's house?
c. Write a proportion using the fractions from parts (a) and (b) to determine how many minutes it takes her to get to the half-way point.
d. Write a two variable equation to represent how many miles Stefanie can drive over any time interval.

Exercise 3
a. Dave lives 15 miles from town A. He is driving at a constant speed of 50 miles per hour from his home away from (in the opposite direction of) the city. How far away is Dave from the town after x hours of driving?

b. The equation that represents how many miles, y, Dave travels after hours x is y = 50x + 15. Use the equation to complete the table below.

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