Question
A person earns 17/5 dollars in 1/2 hours. What is the unit rate in dollars per hour?
645 dollars/hour
512 dollars/hour
412 dollars/hour
312 dollars/hour
645 dollars/hour
512 dollars/hour
412 dollars/hour
312 dollars/hour
Answers
GPT-4o mini
To find the unit rate in dollars per hour, we start with the earnings of \( \frac{17}{5} \) dollars in \( \frac{1}{2} \) hours.
First, we calculate how much the person earns in one hour. Since they earn \( \frac{17}{5} \) dollars in \( \frac{1}{2} \) hours, we can find the rate per hour by using the formula:
\[
\text{Rate} = \frac{\text{Earnings}}{\text{Time}}
\]
Given that time in hours is \( \frac{1}{2} \):
\[
\text{Rate} = \frac{\frac{17}{5}}{\frac{1}{2}}
\]
To divide by a fraction, we multiply by its reciprocal:
\[
\text{Rate} = \frac{17}{5} \times \frac{2}{1} = \frac{17 \times 2}{5 \times 1} = \frac{34}{5}
\]
Now, to express this as a decimal or in simpler terms, we perform the division of \( 34 \) by \( 5 \):
\[
\frac{34}{5} = 6.8
\]
Thus, the unit rate is:
\[
6.8 \text{ dollars per hour}
\]
Now let's match this to the options provided:
- 645 dollars/hour
- 512 dollars/hour
- 412 dollars/hour
- 312 dollars/hour
Since \( 6.8 \) does not match any of the options, it appears there is a misunderstanding in either the problem or the answer choices. The calculated unit rate is indeed \( 6.8 \) dollars per hour based on the provided values. None of the answer choices are correct based on the calculation.
First, we calculate how much the person earns in one hour. Since they earn \( \frac{17}{5} \) dollars in \( \frac{1}{2} \) hours, we can find the rate per hour by using the formula:
\[
\text{Rate} = \frac{\text{Earnings}}{\text{Time}}
\]
Given that time in hours is \( \frac{1}{2} \):
\[
\text{Rate} = \frac{\frac{17}{5}}{\frac{1}{2}}
\]
To divide by a fraction, we multiply by its reciprocal:
\[
\text{Rate} = \frac{17}{5} \times \frac{2}{1} = \frac{17 \times 2}{5 \times 1} = \frac{34}{5}
\]
Now, to express this as a decimal or in simpler terms, we perform the division of \( 34 \) by \( 5 \):
\[
\frac{34}{5} = 6.8
\]
Thus, the unit rate is:
\[
6.8 \text{ dollars per hour}
\]
Now let's match this to the options provided:
- 645 dollars/hour
- 512 dollars/hour
- 412 dollars/hour
- 312 dollars/hour
Since \( 6.8 \) does not match any of the options, it appears there is a misunderstanding in either the problem or the answer choices. The calculated unit rate is indeed \( 6.8 \) dollars per hour based on the provided values. None of the answer choices are correct based on the calculation.