Lesson 10 NYS COMMON COR E MATHEMATICS CURRICULUM 8β’4 Lesson 10: A Critical Look at Proportional Relationships Exit Ticket Sample Solutions Alex skateboards at a constant speed from his house to school π.π miles away. It takes him ππ minutes. a. What fraction represents his constant speed, πͺ? π. π =πͺ ππ b. After school, Alex skateboards at the same constant speed to his friendβs house. It takes him ππ minutes. Write the fraction that represents constant speed, πͺ, if he travels a distance of π. π =πͺ ππ c. Write the fractions from parts (a) and (b) as a proportion, and solve to find out how many miles Alexβs friendβs house is from school. Round your answer to the tenths place. π.π π = ππ ππ π. π (ππ) = πππ ππ = πππ ππ =π ππ π.π β π Alexβs friend lives about π.π miles from school. Lesson 10: A Critical Look at Proportional Relationships This work is derived from Eureka Math β’ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org This file derived from G8-M4-TE-1.3.0-09.2015 112 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Lesson 10 NYS COMMON COR E MATHEMATICS CURRICULUM 8β’4 Problem Set Sample Solutions Students practice writing and solving proportions to solve constant speed problems. Students write two variable equations to represent situations, generally. 1. Eman walks from the store to her friendβs house, π miles away. It takes her ππ minutes. a. What fraction represents her constant speed, πͺ? π =πͺ ππ b. Write the fraction that represents her constant speed, πͺ, if she walks π miles in ππ minutes. π =πͺ ππ c. Write and solve a proportion using the fractions from parts (a) and (b) to determine how many miles she walks after ππ minutes. Round your answer to the hundredths place. π π = ππ ππ πππ = ππ ππ ππ π= ππ ππ π = π. πππππβ¦ Eman walks about π. ππ miles after ππ minutes. d. Write a two-variable equation to represent how many miles Eman can walk over any time interval. Let π represent the distance Eman walks in π minutes. π π = ππ π πππ = ππ ππ π π= π ππ ππ π π= π ππ 2. Erika drives from school to soccer practice π. π miles away. It takes her π minutes. a. What fraction represents her constant speed, πͺ? π. π =πͺ π b. What fraction represents her constant speed, πͺ, if it takes her π minutes to drive exactly π mile? π =πͺ π c. Write and solve a proportion using the fractions from parts (a) and (b) to determine how much time it takes her to drive exactly π mile. Round your answer to the tenths place. π.π π = π π π. ππ = π Lesson 10: A Critical Look at Proportional Relationships This work is derived from Eureka Math β’ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org This file derived from G8-M4-TE-1.3.0-09.2015 113 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Lesson 10 NYS COMMON COR E MATHEMATICS CURRICULUM 8β’4 π.π π π= π.π π. π π = π. πππππβ¦ It takes Erika about π.π minutes to drive exactly π mile. d. Write a two-variable equation to represent how many miles Erika can drive over any time interval. Let π be the number of miles Erika travels in π minutes. π. π π = π π ππ = π.ππ π π.π π= π π π π.π π= π π 3. Darla drives at a constant speed of ππ miles per hour. a. If she drives for π miles and it takes her π hours, write the two-variable equation to represent the number of miles Darla can drive in π hours. π = ππ π π = πππ b. Darla plans to drive to the market ππ miles from her house, then to the post office π miles from the market, and then return home, which is ππ miles from the post office. Assuming she drives at a constant speed the entire time, how long will it take her to run her errands and get back home? Round your answer to the hundredths place. Altogether, Darla plans to drive ππ miles because ππ + π + ππ = ππ. ππ = πππ ππ ππ = π ππ ππ π.πππππβ¦ = π It will take Darla about π.ππ hours to run her errands and get back home. 4. Aaron walks from his sisterβs house to his cousinβs house, a distance of π miles, in ππ minutes. How far does he walk in ππ minutes? I cannot say for sure how far Aaron walks in ππ minutes because I do not know if he is walking at a constant speed. Maybe he stopped at his friendβs house for ππ minutes. 5. Carlos walks π miles every night for exercise. It takes him exactly ππ minutes to finish his walk. a. Assuming he walks at a constant rate, write an equation that represents how many miles, π, Carlos can walk in π minutes. Since π ππ = πͺ and π π = πͺ, then π π = ππ π πππ = ππ Lesson 10: A Critical Look at Proportional Relationships This work is derived from Eureka Math β’ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org This file derived from G8-M4-TE-1.3.0-09.2015 114 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Lesson 10 NYS COMMON COR E MATHEMATICS CURRICULUM 8β’4 ππ π π= π ππ ππ π π= π. ππ b. Use your equation from part (a) to complete the table below. Use a calculator, and round all values to the hundredths place. π (minutes) Linear Equation: π π= π ππ π (miles) ππ π= π ( ππ ) ππ π.ππ ππ π= π ( ππ ) ππ π.ππ ππ π= π ( ππ ) ππ π.ππ ππ π= π ( ππ ) ππ π.ππ ππ π= π ( ππ ) ππ π.ππ Lesson 10: A Critical Look at Proportional Relationships This work is derived from Eureka Math β’ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org This file derived from G8-M4-TE-1.3.0-09.2015 115 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
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