For more information, please see full course syllabus of Pre Algebra

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For more information, please see full course syllabus of Pre Algebra

For more information, please see full course syllabus of Pre Algebra

### Application of Rates

- A rate is a ratio that compares quantities measured in different units; you can use rates to solve problems such as determining distance traveled given a rate and time.
- Average speed is calculated by dividing the total distance traveled by the total amount of time.
- You can use rates to determine a total distance traveled.

### Application of Rates

John drives at 65 mi/hr to the beach, which takes him 1.5 hr. He then drives to the store at 30 mi/hr, which takes him 20 min. What is the total distance John traveled?

- Total distance = distance to the beach + distance to the store
- Distance to the beach = [(65 mi)/(1 hr)] × 1.5 hr =
- 97.5 mi
- Distance to the store = [(30 mi)/(1 hr)] ×[(1 hr)/(60 min)] ×20 min =
- 10 mi
- Total distance = 97.5 mi + 10 mi =

107.5 mi

A car travels from point A to B at 65 mi/hr for 1.5 hr. It then travels from point B to C at 25 mi/hr for 1 hr. What is the car's average speed over the total distance it traveled?

- Average speed = [total distance/total time]
- Total distance = distance from A to B + distance from B to C
- Distance from A to B = [(65 mi)/(1 hr)] × 1.5 hr =
- 97.5 mi
- Distance from B to C = [(25 mi)/(1 hr)] × 1 hr =
- 25 mi
- Total distance = 97.5 mi + 25 mi =
- 122.5 mi
- Total time = time from A to B + time from B to C
- Total time = 1.5 hr + 1 hr =
- 2.5 hr
- Average speed = [(122.5 mi)/(2.5 hr)] =

49 mi/hr

The distance a spring stretches varies directly with the force applied to it. A 10 - lb weight stretches a spring 15 in. How far will a 25 - lb weight stretch the spring?

- [(10 lb)/(15 in)] = [(25 lb)/(x in)]
- 10x = 25 ×15
- 10x = 375

x = 37.5 in

12 cans of soda cost $ 8. How much does 20 cans of soda cost?

- [(16 cans)/$ 8] = [(20 cans)/(x dollars)]
- 16x = 20 ×8
- 16x = 160

x = $ 10

The cost of 5 pairs of socks is $ 25. How many pairs of socks could you buy with $ 15?

- [(5 pairs)/$ 25] = [(x pairs)/$ 15]
- 25x = 5 ×15
- 25x = 75

x = 3 pairs

A cyclist traveled uphill at 8 mi/hr for 5 hr and downhill at 20 mi/hr for 4 hr. What is the average speed of the cyclist?

- Average speed = [total distance/total time]
- Total distance = distance uphill + distance downhill
- Distance uphill = [(8 mi)/(1 hr)] × 5 hr =
- 40 mi
- Distance downhill = [(20 mi)/(1 hr)] × 4 hr =
- 80 mi
- Total distance = 40 mi + 80 mi =
- 120 mi
- Total time = time uphill + time downhill
- Total time = 5 hr + 4 hr =
- 9 hr
- Average speed = [(120 mi)/(9 hr)] =

13[1/3] mi/hr

A truck drive drove on the freeway at 55 mi/hr for 3 hr and on the local streets at 30 mi/hr for 1 hr. What is the average speed of the truck driver?

- Average speed = [total distance/ total time]
- Total distance = distance on the freeway + distance on local streets
- Distance on the freeway = [55 mi/1 hr] ×3 hr =
- 165 mi
- Distance on local streets = [30 mi/1 hr] ×1 hr =
- 30 mi
- Total distance = 165 mi + 30 mi =
- 195 mi
- Total time = time on freeway + time on local streets
- Total time = 3 hr + 1 hr =
- 4 hr
- Average speed = [195 mi/4 hr] =

48[3/4] mi/hr

Michelle drives at 70 mi/hr to a theme park, which takes her 1.2 hr. She then drives to her friend's house at 35 mi/hr, which takes her 30 min. What is the total distance Michelle traveled?

- Total distance = distance to the theme park + distance to her friend's house
- Distance to the theme park = [70 mi/1 hr] ×1.2 hr =
- 84 mi
- Distance to her friend's house = [35 mi/1 hr] ×[1 hr/60 min] ×30 min =
- 17.5 mi
- Total distance = 84 mi + 17.5 mi =

101.5 mi

Eric runs at 6 mi/hr to the bank, which takes him 10 min. He then walks to a restaurant at 4 mi/hr, which takes him 30 min. What is the total distance Eric traveled?

- Total distance = distance to the bank + distance to the restaurant
- Distance to the bank = [6 mi/1 hr] ×[1 hr/60 min] ×10 min =
- 1 mi
- Distance to the store = [4 mi/1 hr] ×[1 hr/60 min] ×30 min =
- 2 mi
- Total distance = 1 mi + 2 mi =

3 mi

Rick needs 3 qt of sugar for a cake he is baking, but he only has cups that measure 2 cups at a time. How many scoops will Rick need to make the cake?

- 3 qt ×[4 cups/1 qt] = 12 cups
- 12 cups ÷ 2 cups =

6 scoops

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

### Application of Rates

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

- Intro 0:00
- What You'll Learn and Why 0:05
- Topics Overview
- Vocabulary 0:18
- Rate
- Unit Rate
- Finding Total Distance 0:32
- Example: Total Distance
- Finding Average Speed 2:49
- Example: Car's Average Speed
- Using a Unit Rate 6:31
- Example: Weight and Spring
- Extra Example 1: Total Distance 8:08
- Extra Example 2: Bird's Average Speed 10:33
- Extra Example 3: Cost of Shirts 13:37
- Extra Example 4: Cost of Bottles 15:22

1 answer

Last reply by: Professor Fung

Sat Dec 1, 2012 4:05 AM

Post by bo young lee on November 29, 2012

i still dont understand the cars average speed question.

can you make more short and simple?

0 answers

Post by Shehan Gunasekara on June 2, 2012

Rad video Bruh!!! :P