Using Reciprocals

Solve for x.

Solve for x.

Solve for x.

Solve for n.

A Tale of One Trucker

Travis Bluster and his brother, Roy, are co-owners of Bluster Brothers Trucking Company. One of their weekly regular summer runs is to transport cantaloupes from Pecos, Texas, where they are grown, to a Dallas distributing plant. Travis knows that his customers are concerned about the speed with which the brothers can deliver the produce, since cantaloupes will spoil after a certain length of time.

Travis wants to be able to address his customer’s concerns with facts and figures. He knows that a typical trip between Pecos and Dallas takes 7.5 hours. He makes the following graph. Use it to answer the questions that follow.

How many miles is Dallas from Pecos How many miles is Dallas from Pecos? Explain how you used the graph to obtain your answer.

Locate the point with coordinates of (3, 270) on the graph, by labeling it point A, and then describe the information these coordinates provide.

According to the graph, how many hours will it take Travis to reach Dallas from Pecos? Explain how you determined your answer.

Interstate 20 is the direct route between Pecos and Dallas Interstate 20 is the direct route between Pecos and Dallas. The posted speed limit for trucks on the interstate is 65 mph. Based upon his graph, at what average speed does Travis expect to travel? Explain how you determined your answer.

Complete the following table to show how far Travis is from Dallas at each hour. Use your table and the graph to write an equation that expresses Travis’ distance d from Dallas, as a function of the elapsed hours h since he left Pecos.

Experience tells Travis that the worst-case scenario would drop his average speed to 45 mph. Travis’s best-case scenario is shown on the grid below. On these same axes, draw the graph of his distance from Dallas, based upon his assumption that he can maintain a 45 mph average speed throughout his trip. Write an equation for the line you drew in response to Question 4.

Travis can average anywhere from 45 mph to 60 mph, as the two previous graphs suggest. On the axes in the Question 4 graph, sketch the vertical line h = 3 and highlight the segment that gives all of his possible distances from Dallas three hours after Travis leaves Pecos. How far might Travis be from Dallas after three hours of travel? Write your answer as an inequality.

Travis can average anywhere from 45 mph to 60 mph, as the two previous graphs suggest. On the axes in the Question 4 graph, sketch the vertical line h = 5 and highlight the segment that gives all of his possible distances from Dallas five hours after Travis leaves Pecos. How far might Travis be from Dallas after five hours of travel? Write your answer as an inequality.