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Chapter 8, Problem 85CQ

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There are 20 cars traveling at constant speeds on a 1 mile long ring track and the cars can pass each other freely. On the track 25% of the cars are traveling at 20 mph, 50% of the cars are traveling 10 mph, and the remaining 25% of the cars are traveling at an unknown speed. It was known that the space mean speed of all the cars on the track is 20 mph. (a) What is the speed that the remaining 25% of cars are traveling at? (b) If an observer standing on the side of the track counted the number and measured the speed of all cars that passed her for one hour, what is the time-mean speed of all the cars the observer counted? (c) What is the flow rate measured by the observer? (d) What is the car density on the track? Does density times space mean speed equal flow rate?

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