MA.FL.7.A.1.6 Apply proportionality to measurement in multiple contexts, including scale drawings and constant speed. Scale Drawing MAPS You may only be given one picture. You will need to read carefully to find the ratios you need for your proportion: The distance from Dover to Butler on the map is 3 inches. The distance from Dover to Lodi on the map is 4 inches. 3inches 4inches 24miles x 24 4 3x 96 3 x x 32 She wants to know the actual distance from Dover to Lodi. Let’s call that x. So Dover is 32 miles from Lodi The paragraph says that the actual distance from Dover to Butler is 24 miles. To find the actual distance on a map or diagram using a scale, think of proportion. Always write the scale as a ratio (as a fraction) first. Then use the information from the problem to write the second ratio (as a fraction). Then cross multiply to find the answer. Aimsworth Scale 1 inch = 20 miles Bellville Haverton On the map, Hector measured a total of 3 inches from Aimsworth to Bellville. Based on the map scale, how many miles is it from Aimsworth to Bellville? 1inch 20miles Write the scale as a ratio: Cross multiply 1inch 3inches = 20miles x Make a proportion or 1inch 3inches = 20miles x 20·3 = 1· x or 60 = x therefore, the actual distance is 60 miles. You can also use proportions for solving speed and distance problems. If Mary took 3 hours and 30 minutes to drive from Orlando to her aunt’s house in Miami, a distance of 210 miles, what was her average speed in miles per hour? Write her time and distance as a ratio: Make a proportion: 210miles (Think, 30 minutes is equal to half an hour.) 3.5hrs 210miles x (Think, the question asks for miles in 1 hour) 3.5hrs 1hr Cross multiply: 210 · 1 = 3.5 · x or 210 = 3.5x divide by 3.5 x = 60 Mary drove an average of 60 miles per hour. MA.FL.7.A.1.6 Practice Problems Try these questions: 1) 2) A scale model racing car is 11 inches long, 3 inches wide, and 2 inches tall. The actual racing car is shown below. How tall is the actual racing car? 3) Using the map in the example above, Hector measured a total of 2 inches from Aimsworth to Haverton. How many miles is it from Aimsworth to Haverton? 4) On a floor plan of your school, your classroom is 9 inches long and 6 inches wide. If the scale is 1 inch = 3 ft., what is the width of your classroom in feet? 5) You have a 4 in. by 5 in. photograph and you want to enlarge it to an 8 in. by 10 in. photograph. Roberto thinks that the new picture is four times as big as the old one. Dora thinks that the new picture is twice as big as the old one. Who is correct? Explain. 6) Dale and his family are planning to fly from Seattle to Miami. The direct flight is 5322 kilometers. Dale drew a line segment on a U.S. map from Seattle to Miami to show his younger sister the flight distance between the two cities. If the scale on the map shows that 2 centimeters represents 600 kilometers, what is the length of the line segment Dale drew on the map from one city to the next? 7) Dominic drove 324 miles from Salt Lake City, Utah, to Bryce Canyon National Park in 6 hours and 45 minutes. What was his average speed, in miles per hour? 8) Jakeem used a scale drawing to build a model airplane. Based on the drawing below, what is the actual length of the plane’s wingspan in feet? 9) Jared and Pedro walk 1 mile in about 15 minutes. They can keep up this pace for several hours. a. About how far do the walk in 90 minutes? b. About how far do they walk in 65 minutes? c. About how far do they walk in 2 hours? 10) Choose the fastest walker: Montel walks 3 miles in 1 hour. Jerry walks 6 miles in 2 hours. Phil walks 6 miles in 1.5 hours. Rosie walks 9 miles in 2 hours. 11) On a long dirt road leading to camp, buses travel only about 6 miles in 10 minutes. a. At this speed, how long does it take buses to travel 18 miles? b. At this speed, how far do the buses go in 15 minutes? 12) The length of an airplane is 87 feet. Find the length of the model of the airplane when 2inches = 15 feet. Find the scale factor. 13) A map of Orlando, Florida, has a scale of 1 inch to 5 miles. If the city is 5 1 inches across on the map, what is the actual 5 distance across the actual city? 14) Jared rode around his neighborhood on in-line skates. He traveled 10 miles in 90 minutes. How many miles does he travel in 3 hours? 15) The Iditarod Snow Dog Race is a famous race in Alaska in which mushers and their dog teams compete. The average speed of the team is about 10 miles per hour. What is the speed in feet per second? 16) The speed at which a certain computer can access the Internet is 2 megabytes per second. How fast is this in megabytes per hour? 17) Water weighs about 8.34 pounds per gallon. About how many ounces per gallon is this?
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