1.4 Applications of Rates

​Applications of Rates
Tutorial

​Objective
In this lesson, you will solve unit rate problems, including those involving unit pricing and constant speed.

​Introduction
Janelle and her family are traveling around Europe. They're spending a few days in Spain and plan to travel to France, Switzerland, and Italy later. When they take a train from Madrid to Barcelona, Janelle asks her brother Andrew how long the journey will take. Andrew tells her that they will reach Barcelona in three hours. Janelle is surprised to see that their train reaches Barcelona in three hours, just as Andrew said. She wonders if there's a relationship between the distance traveled and the time taken. In this lesson, you'll relate the distance traveled to the time taken using a rate. You'll also study how rates apply to other everyday situations. Watch the video on the next screen how a rate can be used to find the speed of a train.

Multiple Choice

Select the correct answer.

Rosemarie drove from Philadelphia, Pennsylvania, to Pittsburgh, Pennsylvania. The distance between Philadelphia and Pittsburgh is 305 miles. Rosemarie reached Pittsburgh 5 hours after she left Philadelphia. What is the speed at which she drove her car?

• • 81 miles/hour

• • 61 miles/hour

• • 51 miles/hour

• • 71 miles/hour

Open Ended

Althea traveled 280 miles at a speed of 70 miles/hour. How much time did she take to cover this distance?

Janelle and her family are traveling around Europe by train. Their trip will begin in Madrid, Spain, and will end in Rome, Italy.

The first part of their train journey, from Madrid, Spain, to Barcelona, Spain, took 3 hours. Use this information to solve the problems below.

Activity

Multiple Choice

Part A

If the train went 390 miles in 3 hours, what was the speed of the train in miles per hour?

( $$usetheformulaspeed=\frac{disance}{time}$$ )

• 130 miles per hour
• 120 miles per hour
• 110 miles per hour
• 100 miles per hour

Multiple Choice

Part B: The distance from Barcelona, Spain, to Paris, France, is 650 miles. If the train from Barcelona to Paris travels 130 miles per hour, how long does it take to get from Barcelona to Paris?

• 5 hours
• 4 hours
• 6 hours
• 7 hours

Multiple Choice

Part C: If the trip from Paris, France, to Geneva, Switzerland, takes 5 hours, and the train travels at 130 miles per hour, how many miles from Paris is Geneva?

• 650 miles
• 500 miles
• 600 miles
• 700 miles

Multiple Choice

Part D: The train from Geneva, Switzerland, to Milan, Italy, travels at 100 miles per hour, and the two cities are 200 miles apart. How long does the journey from Geneva to Milan take?

• 1 hour
• 2 hours
• 3 hours
• 4 hours

Multiple Choice

Part E: If the train from Milan, Italy, to Rome, Italy, takes 6 hours at a speed of 130 miles per hour, how many miles from Milan is Rome?

• 780 miles
• 650 miles
• 520 miles
• 390 miles

Multiple Choice

Part F: Janelle’s parents got a special offer of $75 per person for each train trip. If there are 4 people in Janelle’s family, what is the total cost of each train trip?

• $300
• $200
• $150
• $100

Multiple Choice

Part G: What is the cost of 5 train trips for all 4 family members?

• $100
• $200
• $300
• $400

Open Ended

Self-Evaluation

How did you do? Rate your work on a scale of 1 to 5, with 5 as the highest score. Then write a brief evaluation of your work below. Note what you learned and what challenged you.

Open Ended

Gaston is buying fruit at a local grocery store. This table shows the cost per pound of each type of fruit. Match each quantity of fruit with its total cost. Drag the items on the left to the correct location on the right.

​Summary
Earlier in this lesson, you saw that Janelle could find the speed of her train, or the rate at which it traveled, using the ratio of the distance and the time. You can apply this concept of rates to find quantities such as the speed of a vehicle, the rate at which a machine operates, the distance a vehicle travels at a constant speed, and the time taken to complete a task at a given rate. You can find the price of any quantity of an item, such as groceries or fuel, if you know the unit price of the item. You can also use unit pricing to calculate wages.

​Congratulations!
You have completed the tutorial
Applications of Rates.