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:

Question

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

To identify the errors the coach made in his analysis, let's break down each statement:

1. He used an incorrect time ratio converting hours to minutes.

   • This statement is correct if he did not convert the time properly. There are 60 minutes in an hour, so he should be using the correct conversion factor. However, since he determined her average speed to be 5.8 miles per hour, this particular statement doesn't apply unless there was a direct conversion error referenced.

2. His units do not cancel.

   • This statement may apply if he confused units while converting, leading to incorrect conclusions. If he did not properly account for unit conversions, this could lead to incorrect conclusions.

3. He used an incorrect distance ratio converting miles to feet.

   • This statement would be true if he made a mistake converting miles to feet. The correct conversion is 1 mile = 5280 feet. If he incorrectly used this factor, this could result in an incorrect average speed in feet per second.

4. He incorrectly concluded that she is not running fast enough.

   • This statement might be true if the coach's conversion calculations were incorrect. If he miscalculated her speed, then the conclusion about whether she exceeded 8.2 feet per second could also be erroneous.

5. He cannot determine her average rate in miles per hour after only 15 minutes.

   • This is incorrect; he can determine her average rate in any time period, including 15 minutes. Average rates can be calculated over any duration as long as you have the total distance covered and the total time taken.

In summary, the errors made by the coach could include:

• The possibility of an incorrect distance ratio converting miles to feet.
• The incorrect conclusion that she is not running fast enough if earlier calculations were wrong or misused.

So the correct answers are:

• He used an incorrect distance ratio converting miles to feet.
• He incorrectly concluded that she is not running fast enough.