Exercise 3 Page 710

We are given a rational function which represents the total time t in hours it takes to travel 240 miles at r miles per hour with a half hour break along the way. t = 240/r+0.5 We want to graph this function. To do so let's recall the general form of a rational function. y=a/x- h+ kWe need to have the asymptotes of the function to graph it. In this form, the asymptotes are the lines x= h and y= k. Let's now identify the values of h and k for our function. t = 240/r+0.5 &⇔ t=240/r- 0+ 0.5 We can see that h= 0 and k= 0.5. Therefore, the asymptotes are the lines x= 0 and y= 0.5. With this in mind, we will make a table of values to plot the graph more easily.

Let's now plot and connect the obtained points with a smooth curve. Since the time and the rate cannot be negative, we will use only Quadrant I to draw the graph.

Great! We drew our function. Finally, we are asked to find the average speed in order for the travel time to be about 4 hours. To do so we will substitute 4 for t into the given equation. Let's do it!

We found that we must travel at an average speed of approximately 68.6 miles per hour to complete our travel in about 4 hours.