Answer :
To determine the approximate number of hours in 72 days on Saturn, let's follow a detailed step-by-step approach:
1. Convert Mixed Numbers to Improper Fractions/Decimals:
- [tex]\(266 \frac{2}{3}\)[/tex] hours can be converted to a decimal: [tex]\(266 + \frac{2}{3} = 266 + 0.6667 \approx 266.6667\)[/tex] hours.
- [tex]\(373 \frac{1}{3}\)[/tex] hours can be converted to a decimal: [tex]\(373 + \frac{1}{3} = 373 + 0.3333 \approx 373.3333\)[/tex] hours.
- [tex]\(426 \frac{2}{3}\)[/tex] hours can be converted to a decimal: [tex]\(426 + \frac{2}{3} = 426 + 0.6667 \approx 426.6667\)[/tex] hours.
- [tex]\(586 \frac{2}{3}\)[/tex] hours can be converted to a decimal: [tex]\(586 + \frac{2}{3} = 586 + 0.6667 \approx 586.6667\)[/tex] hours.
2. Record Corresponding Days:
- 25 days for [tex]\(266.6667\)[/tex] hours
- 35 days for [tex]\(373.3333\)[/tex] hours
- 40 days for [tex]\(426.6667\)[/tex] hours
- 55 days for [tex]\(586.6667\)[/tex] hours
3. Calculate the Ratio of Hours per Day for Each Pair:
[tex]\[ \text{Ratio for first entry} = \frac{266.6667 \text{ hours}}{25 \text{ days}} = 10.6667 \text{ hours/day} \][/tex]
[tex]\[ \text{Ratio for second entry} = \frac{373.3333 \text{ hours}}{35 \text{ days}} = 10.6667 \text{ hours/day} \][/tex]
[tex]\[ \text{Ratio for third entry} = \frac{426.6667 \text{ hours}}{40 \text{ days}} = 10.6667 \text{ hours/day} \][/tex]
[tex]\[ \text{Ratio for fourth entry} = \frac{586.6667 \text{ hours}}{55 \text{ days}} = 10.6667 \text{ hours/day} \][/tex]
4. Calculate the Average Ratio of Hours per Day:
[tex]\[ \text{Average ratio} = \frac{10.6667 + 10.6667 + 10.6667 + 10.6667}{4} = 10.6667 \text{ hours/day} \][/tex]
5. Determine the Number of Hours for 72 Days Using the Average Ratio:
[tex]\[ \text{Hours for 72 days} = 72 \text{ days} \times 10.6667 \frac{\text{hours}}{\text{day}} = 768 \text{ hours} \][/tex]
Therefore, the approximate number of hours in 72 days on Saturn is 768 hours.
1. Convert Mixed Numbers to Improper Fractions/Decimals:
- [tex]\(266 \frac{2}{3}\)[/tex] hours can be converted to a decimal: [tex]\(266 + \frac{2}{3} = 266 + 0.6667 \approx 266.6667\)[/tex] hours.
- [tex]\(373 \frac{1}{3}\)[/tex] hours can be converted to a decimal: [tex]\(373 + \frac{1}{3} = 373 + 0.3333 \approx 373.3333\)[/tex] hours.
- [tex]\(426 \frac{2}{3}\)[/tex] hours can be converted to a decimal: [tex]\(426 + \frac{2}{3} = 426 + 0.6667 \approx 426.6667\)[/tex] hours.
- [tex]\(586 \frac{2}{3}\)[/tex] hours can be converted to a decimal: [tex]\(586 + \frac{2}{3} = 586 + 0.6667 \approx 586.6667\)[/tex] hours.
2. Record Corresponding Days:
- 25 days for [tex]\(266.6667\)[/tex] hours
- 35 days for [tex]\(373.3333\)[/tex] hours
- 40 days for [tex]\(426.6667\)[/tex] hours
- 55 days for [tex]\(586.6667\)[/tex] hours
3. Calculate the Ratio of Hours per Day for Each Pair:
[tex]\[ \text{Ratio for first entry} = \frac{266.6667 \text{ hours}}{25 \text{ days}} = 10.6667 \text{ hours/day} \][/tex]
[tex]\[ \text{Ratio for second entry} = \frac{373.3333 \text{ hours}}{35 \text{ days}} = 10.6667 \text{ hours/day} \][/tex]
[tex]\[ \text{Ratio for third entry} = \frac{426.6667 \text{ hours}}{40 \text{ days}} = 10.6667 \text{ hours/day} \][/tex]
[tex]\[ \text{Ratio for fourth entry} = \frac{586.6667 \text{ hours}}{55 \text{ days}} = 10.6667 \text{ hours/day} \][/tex]
4. Calculate the Average Ratio of Hours per Day:
[tex]\[ \text{Average ratio} = \frac{10.6667 + 10.6667 + 10.6667 + 10.6667}{4} = 10.6667 \text{ hours/day} \][/tex]
5. Determine the Number of Hours for 72 Days Using the Average Ratio:
[tex]\[ \text{Hours for 72 days} = 72 \text{ days} \times 10.6667 \frac{\text{hours}}{\text{day}} = 768 \text{ hours} \][/tex]
Therefore, the approximate number of hours in 72 days on Saturn is 768 hours.
