4.2+Changing+Speeds+0910

Ajwad Khan Sep. 26, 09 Math 7B Problem 4.2


 * A.** **Make of 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.**

· The similarity of the 3 tables of distance is that each of them is increasing by the same each time. What is different is that each is increasing by a different number.
 * Plot the data from both tables on one coordinate grid. Use a different color for each set of data. Using a third color, add data points for the times an****d distances traveled at 55 miles per hour (from Problem 4.1)**
 * Time (hours) || 0 || 1 || 2 || 3 || 4 || 5 || 6 || 7 || 8 || 9 || 10 ||
 * Distance: 50 mph (miles) || 0 || 50 || 100 || 150 || 200 || 250 || 300 || 350 || 400 || 450 || 500 ||
 * Distance: 65 mph (miles) || 0 || 65 || 130 || 195 || 260 || 325 || 390 || 455 || 520 || 585 || 650 ||
 * B. How are the tables for the 3 speeds similar? How are they different?**

· The similarity of the different graphs of distance is that they are all going at a steady pace. Meaning that the lines are all going up across the graph in a straight line. The only thing different about the graphs is that the lines are heading in different directions because the speed is different so the distance is also different.
 * C. How are the graphs for the 3 speeds similar? How are they different?**

1) To find the distance of any given time when going at 65 miles per hour, you have to multiply the number of hours by 65 because each hour added adds another 65 miles.
 * 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 the distance for any given time.**

2) D=65h · D is for distance · 65 means the speed in miles · h is for hours
 * 2. Use symbols to write your rule as an equation.**

1) To calculate the distance of any given time when going at 50 miles per hour, you must multiply the number of hours by 50. 2) D=50h · D is for distance · 50 is the speed in miles · h is for hours
 * 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.**
 * 2. Use symbols to write your rule as an equation.**

· The 3 speeds have a similar rule because they are all using the same method in which they multiply the speed by the number of hours. They are different because they are different speeds and you must multiply by different numbers. Problem 4.2 Follow-Up · Malcolm’s equation is saying the distance equals whatever the time was multiplied by 60.
 * F. How are the rules for calculating distance for the 3 speeds similar? How are they different?**
 * 1. After arriving in Philadelphia, Malcolm took the interest home. He wrote the equation d=60t to represent his trip home. Explain this equation in words.**

· At 50 miles per hour it would take about 6 hours to travel 310 miles. At 60 miles per hour it would take about 5 hours and at 65 miles per hour it would take about 4.5 hours to travel 310 miles.
 * 2. 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?**