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.

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1986 AJHSME Problems/Problem 1

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