which of the following best represents the average speed of a fast runner?

Usain Bolt traveled 328 feet in 9.63 seconds.

Usain Bolt traveled 100 meters in 9.63 seconds.

The method used here first finds how many feet per second Usain Bolt is running and then moves from here to miles per hour. In this solution, each successive line in the table represents a single unit conversion, either for distance or for time. We can make a table of distances and times and then find the corresponding rate at the end. Given the complexity of the problem, it would not be appropriate for high-stakes summative assessment but would be very appropriate in an instructional setting. Also, given the number of steps required to solve this problem, it is well aligned to MP1, Make sense of problems and persevere in solving them. Note that both the time for the 100 meter race and the conversion from meters to feet are given with three digit, so only three digits should remain in the answer. The relevant practice standards for this problem are MP2, Reason abstractly and quantitatively, as students move between the context and the calculations, and MP6, Attend to precision, as students must focus on units and the accuracy with which they present their final answer. For a more creative implementation of this task, the teacher could provide the table of different animal speeds and ask the students how the fastest human beings would fair against them in a race. Note that the speed calculated in this problem is the average speed for 100 meters which is a little less than the top speed, but 23mph is significantly less than any of the other animals on the list. Remarkably, of the animals in the table, the fastest human beings can only run faster than the hippopotamus. In addition to the work on conversion of units, it might be interesting to compare the top speed of the fastest human being to some familiar animals: The second solution goes step by step and provides an excellent opportunity to discuss rounding error as it is important here to make all calculations (as in the first method) before rounding rather than using the rounded numbers for successive calculations. The first solution shows all units in the calculations and does not make any calculations until the end. Most of us are used to thinking about speeds in terms of miles per hour since the speedometers in our automobiles use these units, so it is good for students to be able to convert between miles per hour and other units for speed that naturally come up. In this case, the units coming from the 100 meter race are meters per second and we do not have a good intuition for what this means in miles per hour. This task involves a multi-step conversion between two rates, going from meters per second to miles per hour.

Which of the following best represents the average speed of a fast runner?