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Average Appearances Can Be Deceiving

Problem A: A man in a car travels at 80 mph for 40 miles, 72 mph for 48 miles, and 96 mph for 32 miles. What is his average rate of speed over the entire trip?

Problem B: A woman drives 30 mph from her house to a store. At what speed must she return home in order to average 60 mph for the entire trip?


Hint: In Problem A, average speed = (total distance)/(total time)...so?

Now, think about the same thing for Problem B.


Solution Commentary: Rather thah provide a solution, I will provide what are NOT answers.

For Problem A, it is not (80+72+96)/3...need to consider idea of a weighted idea, weighted by the amount of time allocated to each speed.

For Problem B, the answer is not a finite number...but how can that be?