4.2+Changing+Speeds+0910

9/11/09 SSB  Problem 4.2 Changing Speeds ** 
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Big Idea: Observation and description of changes in the world around us are the first steps in finding and learning about patterns.  INV 4 Essential Question: How can I use graphs, tables and symbols to solve problems.  ======

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 Notes:  I learned how to use equations.======

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 * A. Make tables of time and distance data, similar to the table you made for problem 4.1, for travel at 50 miles per hour and 65 miles per hour. ** **Plot the data from both the tables on one coordinate grid. Use a different color for each set of data. Using a third color, add data points for the times and distances traveled at 55 miles per hour (From problem 4.1). ** [[image:ssbtable.JPG]][[image:ssbtable2.JPG]] ======



All the tables start at zero but they all ended up at different numbers. They also had different distance intervals.
 * B. How are the tables for the three speeds similar? How are they different?**

The graphs all had steady increase rates(that's why I connected the points)but each had its own angle of increase.
 * C. How are the graphs for the three speeds similar? How are they different?**

You just multiply the time by 65 miles to find the distance. <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; line-height: 150%; mso-fareast-font-family: 'Times New Roman';"> The equations are: //d=65h// & //d=sh// The data increases by 65 miles per interval.
 * D. 1. Look at the table and graph for 65 miles per hour. What pattern of change in the data helps you calculate the distance for any given time? In words, write a rule that explains how to calculate distance for any given time.** <span style="font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 150%; mso-fareast-font-family: 'Times New Roman';">
 * 2. Use symbols to write your rule as an equation.**

Multiply the time by 50 miles to find the distance.
 * E. 1. Now write a rule, in words, that explains how to calculate the distance traveled for any given time when the speed is 50 miles per hour.**

//d=sh & d=50h// All of the speeds have the same general equation //d=sh// but they all have different speeds, like //d=50h, d=65h,// and //d=55h.//
 * 2.Use symbols to write your rule as an equation.**
 * F. How are the rules for calculating the three speeds similar? How are they different?**


 * Problem 4.2 Follow Up** <span style="font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 150%; mso-fareast-font-family: 'Times New Roman';">

<span style="font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 150%; mso-bidi-font-size: 28.0pt; mso-fareast-font-family: 'Times New Roman';">The equation //d=60t// means that Malcolm was going at a steady speed of 60 miles per hour. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 150%; mso-fareast-font-family: 'Times New Roman';"> <span style="font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 150%; mso-bidi-font-size: 28.0pt; mso-fareast-font-family: 'Times New Roman';"> **<span style="font-family: 'Times New Roman','serif'; font-size: 12pt; line-height: 150%; mso-fareast-font-family: 'Times New Roman';"> 2. **<span style="font-family: 'Times New Roman','serif'; font-size: 7pt; line-height: 150%; mso-bidi-font-size: 28.0pt; mso-fareast-font-family: 'Times New Roman';"> **<span style="font-family: 'Times New Roman','serif'; font-size: 12pt; line-height: 150%; mso-fareast-font-family: 'Times New Roman';">How long would it take to reach Philadelphia-310 miles from Williamsburg-traveling at 50 miles per hour? 60 miles per hour? 65 miles per hour? **<span style="font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 150%; mso-fareast-font-family: 'Times New Roman';"> It would take them about 5 hours to get to Philadelphia from Williamsburg at 60 miles per hour <span style="font-family: Vrinda; font-size: 12.5pt; line-height: 150%; mso-ansi-font-size: 10.0pt; mso-ascii-font-family: Arial; mso-bidi-language: BN-BD; mso-fareast-font-family: 'Times New Roman'; mso-hansi-font-family: Arial;">, <span style="font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 150%; mso-fareast-font-family: 'Times New Roman';"> 4 and 1/2 hours at 65 miles per hour and a bit more than 6 hours at 50 miles per hour.
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; line-height: 150%; mso-fareast-font-family: 'Times New Roman';">1. **<span style="font-family: 'Times New Roman','serif'; font-size: 7pt; line-height: 150%; mso-bidi-font-size: 28.0pt; mso-fareast-font-family: 'Times New Roman';"> **<span style="font-family: 'Times New Roman','serif'; font-size: 12pt; line-height: 150%; mso-fareast-font-family: 'Times New Roman';">After arriving in Philadelphia, Malcolm took the interstate home. He wrote the equation //d//=60//t// to represent his trip home. Explain this equation in words. **<span style="font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 150%; mso-fareast-font-family: 'Times New Roman';">