Question: In a certain city, it was recorded that 10 6/7 inches of rain fell over a 24-hour period. How much rain fell per hour on average?
On average, □ inches of rain fell per hour.
1. **State the problem:** We need to find the average rainfall per hour given that 10 6/7 inches of rain fell over 24 hours.
2. **Convert the mixed number to an improper fraction:**
$$10 \frac{6}{7} = \frac{10 \times 7 + 6}{7} = \frac{70 + 6}{7} = \frac{76}{7}$$
3. **Use the formula for average rate:**
$$\text{Average rain per hour} = \frac{\text{Total rain}}{\text{Total time}}$$
4. **Substitute the values:**
$$= \frac{\frac{76}{7}}{24}$$
5. **Divide the fraction by 24:**
$$= \frac{76}{7} \times \frac{1}{24} = \frac{76}{7 \times 24} = \frac{76}{168}$$
6. **Simplify the fraction:**
Find the greatest common divisor (GCD) of 76 and 168, which is 4.
$$\frac{\cancel{4} \times 19}{\cancel{4} \times 42} = \frac{19}{42}$$
7. **Convert to decimal (optional):**
$$\frac{19}{42} \approx 0.4524$$
**Final answer:**
On average, $$\frac{19}{42}$$ inches of rain fell per hour, approximately $$0.4524$$ inches per hour.