Question

A person earns 17/5 dollars in 1/2 hours. What is the unit rate in dollars per hour?
6 4/5 dollars/hour
5 1/2 dollars/hour
4 1/2 dollars/hour
3 1/2 dollars/hour

Answer 1

To find the unit rate in dollars per hour, we first need to determine how much the person earns in one hour.

The person earns \( \frac{17}{5} \) dollars in \( \frac{1}{2} \) hours.

To find the hourly rate, we can use the formula:

\[
\text{Unit rate (dollars/hour)} = \frac{\text{Earnings}}{\text{Time in hours}}
\]

In this case:

\[
\text{Unit rate} = \frac{\frac{17}{5}}{\frac{1}{2}}
\]

To divide fractions, we multiply by the reciprocal:

\[
\text{Unit rate} = \frac{17}{5} \times \frac{2}{1} = \frac{34}{5}
\]

Next, we can convert \( \frac{34}{5} \) to a mixed number:

\[
34 \div 5 = 6 \quad \text{(whole number)}
\]
\[
34 - (5 \times 6) = 4 \quad \text{(remainder)}
\]

So, \( \frac{34}{5} = 6 \frac{4}{5} \).

Thus, the unit rate is:

\[
\boxed{6 \frac{4}{5} \text{ dollars/hour}}
\]