Aliza needs to run at a rate faster than 8.8 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. What errors did the coach make? Check all that apply.

The rate at which she runs is referred to as speed. The need for Aliza to run faster means she has to increase her speed from 8.8ft/s to a greater speed. Her coach's errors are:

Error in converting hour to seconds
Error in making conclusions

Given that:

[tex]r = 8.8ft/s[/tex] --- rate to beat

[tex]t = 15mins[/tex] --- time

[tex]r_c = 5.8mi/hr[/tex] --- current rate per hour

The coach's conversion is as follows:

[tex][\frac{5.8mi}{hr}] \times [\frac{1hr}{15min}] \times [\frac{5280ft}{1mi}] \times [\frac{1min}{60s}] = 34.0 \frac{ft}{s}[/tex]

The first error is the hour to second conversion:

The conversion from hour to second is wrong because:

[tex]1\ hr = 3600\ s[/tex]

But he used

[tex]1\ hr = 60\ s[/tex]

Another error the coach made is that:

The result of his conversion is 34.0ft/s; his conclusion should be that she is running fast enough because 34.0ft/s is greater than 8.8ft/s/

Hence, his second error is incorrect conclusion.