To find out how much time Rosalie spends exercising in a week, we will first calculate her daily exercise time in minutes and then multiply that by the number of days in a week.
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Convert Rosalie's exercise time to minutes: \[ \text{Exercise time in minutes} = \frac{2}{5} \text{ hours} \times 60 \text{ minutes/hour} = \frac{2 \times 60}{5} = \frac{120}{5} = 24 \text{ minutes} \]
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Calculate the weekly exercise time: \[ \text{Weekly exercise time} = 24 \text{ minutes/day} \times 7 \text{ days} = 168 \text{ minutes} \]
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Convert 168 minutes to hours and minutes:
- Convert to hours: \( 168 \div 60 = 2 \) hours (since \( 60 \times 2 = 120 \))
- Remaining minutes: \( 168 - 120 = 48 \) minutes
So, Rosalie spends a total of 2 hours and 48 minutes exercising in a week.
- Convert to a mixed number:
- The answer in mixed number form is \( 2 \frac{48}{60} \).
- We can simplify \(\frac{48}{60}\) to \(\frac{4}{5}\) (since the GCD of 48 and 60 is 12).
- The mixed number becomes \( 2 \frac{4}{5} \).
Thus, the final answer is:
\[ \boxed{2 \frac{4}{5}} \]
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