Let's analyze the problem and identify the errors made by the coach.
1. He used an incorrect time ratio converting hours to minutes.
- The correct conversion ratio from hours to minutes is 60 minutes in 1 hour.
2. His units do not cancel.
- In the expression provided, it appears the coach has mixed units in such a way that they do not properly cancel out or represent the measurements accurately.
3. He used an incorrect distance ratio converting miles to feet.
- The correct conversion from miles to feet is 5280 feet in 1 mile.
4. He incorrectly concluded that she is not running fast enough.
- To verify this, we need to convert 5.8 miles per hour to feet per second using correct ratios:
- 1 mile = 5280 feet
- 1 hour = 3600 seconds
[tex]\[\text{Average rate in feet per second} = \frac{5.8 \text{ miles/hour} \times 5280 \text{ feet/mile}}{3600 \text{ seconds/hour}} \approx 8.51 \text{ feet/second}\][/tex]
Since 8.51 feet per second is greater than the required 8.2 feet per second, she is indeed running fast enough.
5. He cannot determine her average rate in miles per hour after only 15 minutes.
- This statement is incorrect. It is possible to determine an average rate over any given time duration, including 15 minutes.
From this detailed analysis, we can identify the following errors made by the coach:
1. Incorrect time ratio conversion.
2. Units do not properly cancel.
3. Incorrect distance ratio conversion.
4. Incorrect conclusion about running speed.
The true errors are:
- 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.
Errors identified:
[tex]\[1, 2, 3, 4\][/tex]
