High-Speed Trains (Continued)Team K

High-Speed Trains (continued)Team K

High-Speed TrainsTeam K

Before You Start

Traveling by high-speed train is common throughout Asia and Europe and is becoming more common in North America. These train lines operate at significantly faster speeds than regular rail traffic.

Activity

You begin your research by looking at unit rates — specifically, at the average speeds of several trains during particular trips.

1.The Asama train connects Tokyo and Nagano in Japan. It travels 210.6 miles in 1.3 hours. What is this train’s average speed?

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2.The Dublin-to-Belfast line in Ireland plans to upgrade its route to make the 187.5-mile trip in 90 minutes. What is the planned average speed of this route in miles per hour?

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3.The Shanghai Maglev Train in China opened in 2004. It travels 19 miles in about 7 minutes.

a.To the nearest tenth of a mile, how many miles can this train travel in one minute?

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b.To the nearest mile per hour, what is this train’s average speed in miles per hour?

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You continue your research by writingan equation that will help you predict the distances that can be traveled in various times.

4.In 2010, the Chinese CRH380A set a speed record with a rate of 302miles per hour on the newly constructed line between Beijing and Shanghai. Write an equation that gives the distance d the train can travel in t hours at its maximum speed.

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Finally, your research has you compare the lengths of the high-speed rail lines in different European countries.

Country / Total Length
of Rail Lines
km / mi
France / 1,896 / 1,185
Germany / 1,285 / 803
Italy / 923 / 577
Spain / 2,056 / 1,285

5.The total lengths of the high-speed rail lines in several European countries are shown at the right.

a.For each country, write the ratio of the total length of the rail networkin kilometers to the total length in miles.Convert each ratio to a decimal rounded to the nearest tenth.

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b.Explain whether a proportional relationship exists between the lengths in kilometers and the lengths in miles.

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6.Portugal has plans to construct a total of 1,006 kilometers ofhigh-speed rail lines. Use the same relationship to determine the proportional number of whole miles for this network.

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7.Quick ReportUse your results from this activity to complete the report below. In the first column, only consider the trains in Questions 1-3.

Fastest Train / Distance d the CRH380A Can Travel in tHours / Ratio of Kilometers to Miles

8.ReflectExplain how you used each skill in this activity.

a.finding unit rates

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b.writing an equation in two variables

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c.recognizing proportional relationships

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– grade 6 • Readiness Lesson

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Working With Playlists (continued)Team G

1.162 mi/h

2.125 mi/h

3.a. 2.7

b. 163 mi/h

4.d = 302t

5.a. France: = 1.6

Germany: ≈ 1.6

Italy: ≈ 1.6

Spain: = 1.6

b. Because the ratios are approximately constant, a proportional relationship exists.

6.629 mi

7.

Fastest Train / Distance d the CRH380A Can Travel in tHours / Ratio of Kilometers to Miles
Asama / d = 302t / 1.6

8.Answers may vary. Sample answers are given.

a.I found unit rates when I calculated the average speeds of different trains.

b.I wrote an equation in two variables when I used the distance formula to represent the distance d a train travels in t hours at its maximum speed.

c.I recognized a proportional relationship when I compared the decimal equivalents of the ratios of the lengths in kilometers to the lengths in miles for rail lines in several European countries.

– grade 6 • Readiness Lesson

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