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.

What errors did the coach make? Check all that apply.

He used an incorrect time ratio converting hours to minutes.
His units do not cancel.
He used an incorrect distance ratio converting miles to feet.
He incorrectly concluded that she is not running fast enough.
He cannot determine her average rate in miles per hour after only 15 minutes.

Answer 1

Hi, and welcome to QuestionCove!
The question you posted doesn't show the method that the coach used, but that's ok. I'll try to demonstrate the correct method for converting miles per hour to feet per second, and you can compare that to the coach's method to find the errors and complete the answer

If Aliza runs 1.45 miles in 15 minutes,
(1.45 mi/15 min) * (60 min/1 hr) =
(1.45 mi * 60 mi/15 min * 1 hr) [minutes units cancel] =
(1.45 * 4 mi/1 hr) = 5.8 mi/hr, as the coach determined.

From here, we can do a similar unit conversion:
(5.8 mi/ hr) * (5280 ft/ 1 mi) * (1 hr/3600 sec) =
(5.8 mi * 5280 ft/ 1 hr * 1 mi) * (1 hr/3600 sec) [miles units cancel] =
(30624 ft/hr) * (1 hr/3600 sec) =
(30624 ft* 1 hr/ hr*3600 sec) [hours units cancel] =
8.51 feet per second

It seems that, based on these calculations, Aliza was indeed running faster than 8.2 feet per second.
So, were you able to see where the coach made his error(s)? If you still are not sure, perhaps you can try posting a copy of the coach's work and we can examine that in more detail together :)