# 1986 AJHSME Problems/Problem 1

## Problem

In July 1861, $366$ inches of rain fell in Cherrapunji, India. What was the average rainfall in inches per hour during that month? $\text{(A)}\ \frac{366}{31\times 24}$ $\text{(B)}\ \frac{366\times 31}{24}$ $\text{(C)}\ \frac{366\times 24}{31}$ $\text{(D)}\ \frac{31\times 24}{366}$ $\text{(E)}\ 366\times 31\times 24$

## Solution

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 $\dfrac{366 \text{ inches}}{31 \times 24 \text{ hours}}$, which is $\boxed{\text{A}}$.

Note that in the simplifying step, we noted that the month and day units cancel, leaving us with only inches per hour.

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 