2.3+Testing+Whether+Driving+Fast+Pays

AS 2.3 TESTING WHETHER DRIVING FAST PAYS Date assingned: 01/09/08

Notes:
 * Essential Question: What are some types of non-linear models?
 * Big Idea: Many real world situations can be predicted and modeled using maths.
 * A bus is going to take the riders of Ocean and History Bicycle tour organization back to home from Williamsburg to Philadelphia which is going to be 300 miles journey. They want to know if driving fast pays.


 * Problem 2.3**

A. **Question: Copy and complete the table below to show the time it would take for the 300-mile trip at various average speeds.** B. **Question: Make a graph of the relationship between the average speed, S, and the time, T.**
 * Average speed(miles) || Trip Time( hours) ||
 * 30 || 10 ||
 * 40 || 7.5 ||
 * 50 || 6 ||
 * 60 || 5 ||
 * 70 || 4.28 ||

C.**Question: Find an equation for the relationship between S and T.**

The equation would be T=300/S because if you multiply all the A's by all the T;s, the product is going to be 300 miles, so the equation would be T=300/S.

D. **Question: Is the relationship between S and T linear or non-linear? Explain how the table, the graph, the equation support you answer?**

The relationship between S and T is non-linear because if you look at the table, you can see that Trip time doesn't decrease by the same amount of value as Average Speed increases by 10, the graph doesn't have a straight line like all linear graphs should have and the equation doesn't have the y=mx+b form.

Problem 2.3 follow-up

1. **Question: The bus driver figured our that if he increased his average speed from 40 to 45 miles per hour, the time for the trip would be shortened from 7 and a1/2 to 6 and 2/3, a savings of 50 minutes. He then reasoned that increasing his average speed from 45 to 50 miles per hour would cut another 50 minutes off the trip, and increasing from 50 to 55 miles per hour would cut another 50 minutes off the trip.**

a. **Question: Do you agree with the bus driver's conclusion about the time he would save by driving faster? Explain your reasoning.**

Yes, I agree with the bus driver 's conclusions about the time he would save by driving faster because 7 and a half hours= 450 minutes and 6 and 2/3=400 minutes, so 450-400=50, so the driver said that that he would save 50 minutes by driving 5 miles faster. So he was correct.

b. **Question: How is your answer for part a illustrated in your graph of the (speed,time) data?**

It is illustrated in the graph by the y-value decreasing at the same amount of number at the 45, to 50 to 55 axis.

2. **Question: How would the table, the graph, and the equation change if the trip were 500 miles instead of 300 miles**? Then the trip time for each average speed would have been higher than the 300-mile trip.

3. **Question: Look back at your work from Problem 2.2. Find an equation for the relationship.

The equation would be y=-0.125x.**