Catch-Up Rate Problem: Willie Ketchup is out for his morning walk. He sees Betty Wont

Chapter 4, Problem 28

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Catch-Up Rate Problem: Willie Ketchup is out for his morning walk. He sees Betty Wont walking ahead of him and decides to catch up to her. He quickly figures that she is walking at a rate of 5 ft/s. He lets x, in ft/s, stand for his walking rate. a. Explain why Willie catches up at the rate of (x 5) ft/s. b. Betty is 300 ft ahead of Willie when he first begins to catch up. Recall that distance = rate time to write an equation for t(x), the number of seconds it will take him to catch up to her. Use the equation to find out how long it will take Willie to catch up if he walks at rates of 6, 8, 10, 5, 4, and 5.1 ft/s. What is a reasonable domain for x? c. What is the instantaneous rate of change of Willies catch-up time if he is going 6 ft/s?What are the units of this rate?d. Explain why t(x) has no value for thederivative at x = 5.