To find out how many hours of homework Olivia does in 5 days, we start with the amount of time she spends on homework each day, which is \( \frac{5}{6} \) of an hour.
Now, we can calculate the total time spent on homework over 5 days by multiplying:
\[ \text{Total homework time} = \frac{5}{6} \times 5 \]
Calculating this gives:
\[ \frac{5 \times 5}{6} = \frac{25}{6} \text{ hours} \]
Next, let's convert \( \frac{25}{6} \) hours into a more understandable form. To do this, we can divide \( 25 \) by \( 6 \):
\[ 25 \div 6 = 4 \quad \text{R} 1 \]
This means that: \[ \frac{25}{6} = 4 \frac{1}{6} \text{ hours} \]
Now, let's convert \( \frac{1}{6} \) of an hour into minutes. Since 1 hour = 60 minutes, we can calculate:
\[ \frac{1}{6} \times 60 = 10 \text{ minutes} \]
Thus, \( \frac{25}{6} \) hours can also be expressed as: \[ 4 \text{ hours and } 10 \text{ minutes} \]
So the total amount of homework Olivia does in 5 days is \( 4 \frac{1}{6} \) hours, or 4 hours and 10 minutes.
Among the given options, the closest match is:
41/2 hours (though this is not exactly correct; the conversion is not represented correctly in the options). The correct answer, based on our calculations, is \( 4 \frac{1}{6} \) hours, or 4 hours and 10 minutes.
None of the provided options precisely match this calculation. However, if the intention was to round or use a specific available choice, 31/2 hours is closer to \( 4 \frac{1}{6} \) than 41/2 hours.
It is important to note that the correct interpretation of 4 hours and 10 minutes has not correctly been reflected by any of the options provided. Please let me know if you would like to clarify, or if there's more information!