Difference between revisions of "1986 AJHSME Problems/Problem 1"
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==Solution== | ==Solution== | ||
| − | We can express the number of inches of rain in a ratio, <math>\frac{366 inches}{1 month}</math>. 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 | + | We can express the number of inches of rain in a ratio, <math>\frac{366 \text{ inches}}{1\text{ month}}</math>. 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 <cmath>\frac{366 \text{ inches}}{1 \text{ month}} \times \frac{1 \text{ month}}{31 \text{ days}}</cmath> |
| − | < | + | We know there are 24 hours in a day, so we get <cmath>\frac{366 \text{ inches}}{1 \text{ month}} \times \frac{1 \text{ month}}{31 \text{ days}} \times \frac{1 \text{ day}}{24 \text{ hours}}</cmath> |
| − | + | And simplifying gets us <math>\dfrac{366 \text{ inches}}{31 \times 24 \text{ hours}}</math>, which is <math>\boxed{\text{A}}</math>. | |
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| − | <math>\ | ||
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| − | <math>\ | ||
Note that in the simplifying step, we noted that the month and day units cancel, leaving us with only inches per hour. | Note that in the simplifying step, we noted that the month and day units cancel, leaving us with only inches per hour. | ||
Revision as of 18:05, 24 January 2009
Problem
In July 1861, 
inches of rain fell in Cherrapunji, India. What was the average rainfall in inches per hour during that month?
Solution
We can express the number of inches of rain in a ratio, 
. 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 ![\[\frac{366 \text{ inches}}{1 \text{ month}} \times \frac{1 \text{ month}}{31 \text{ days}}\]](http://latex.artofproblemsolving.com/e/4/7/e47c78f8893cf81d05f3720052b63b88cdadd5f0.png)
We know there are 24 hours in a day, so we get ![\[\frac{366 \text{ inches}}{1 \text{ month}} \times \frac{1 \text{ month}}{31 \text{ days}} \times \frac{1 \text{ day}}{24 \text{ hours}}\]](http://latex.artofproblemsolving.com/3/9/d/39d190cbf01f0e5c1301dbd3c0fc11ae31016fb7.png)
And simplifying gets us 
, which is 
.
Note that in the simplifying step, we noted that the month and day units cancel, leaving us with only inches per hour.
