Question

Aliza needs to run at a rate faster than 8.2 feet per second in order to exceed her fastest time in a race. After running for 15 minutes, her coach determines that she is running at an average rate of 5.8 miles per hour. He converts the average rate to feet per second as shown below:
He concludes that she is not running fast enough to exceed her fastest time.

Answer 1

The coach's errors are;

• Wrong conversion when converting hour to seconds
• The wrong conclusion since Eliza was running fast enough at a speed of 34ft/s compared to 8.8ft/s

What is speed?

Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance.

Given the speed that Aliza needs to run in order to exceed her fastest time in a race = 8.8 feet per second

If her coach determines that she is running at an average rate of 5.8 miles per hour, we need to first convert the speed her coach assumed to feet per second

Convert 5.8miles to feet per second

According to the coach's conversion

$=5.8\times \dfrac{1}{15}\times 5280\times \dfrac{1}{60}$

This shows that 5.8mi/hr is equivalent to 34.0ft/s according to the coach conversion rate.

From the coach's calculation, we see that the coach made the first error by using 60s as 1hr instead of 3600s as 1hr

The coach also made an error by saying Eliza is not running fast enough to exceed her fastest time. We can see that Eliza was running fast enough since her speed at 34ft/s exceed 8.8ft/s.

Hence the second error was a wrong conclusion made by the coach.

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