jmc

We can express the number of inches of rain in a ratio, $\frac{366\text{ inches}}{1\text{ month}}$. We need to find to find the number of hours, but first we need to find the number of days. We know there are 31 days in July, so we get $$\frac{366\text{ inches}}{1\text{ month}}\times \frac{1\text{ month}}{31\text{ days}}$$ We know there are 24 hours in a day, so we get $$\frac{366\text{ inches}}{1\text{ month}}\times \frac{1\text{ month}}{31\text{ days}}\times \frac{1\text{ day}}{24\text{ hours}}$$ And simplifying gets us $\frac{366\text{ inches}}{31\times 24\text{ hours}}$, which is $\boxed{\frac{366}{31\times 24}}$. Note that in the simplifying step, we noted that the month and day units cancel, leaving us with only inches per hour.