Difference between revisions of "2023 AMC 8 Problems/Problem 11"
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− | == | + | ==Solution 1== |
Since the answers are so far apart, we just need to compute the # of figures the answer contains. So by approximating all the values for the hourly rate we have <math>\frac{300,000,000}{5 * 30 * 30} \approx \frac{300,000,000}{5000} = 60,000</math> which is <math>\boxed{\text{(C)}60,000}</math> | Since the answers are so far apart, we just need to compute the # of figures the answer contains. So by approximating all the values for the hourly rate we have <math>\frac{300,000,000}{5 * 30 * 30} \approx \frac{300,000,000}{5000} = 60,000</math> which is <math>\boxed{\text{(C)}60,000}</math> | ||
~apex304 | ~apex304 | ||
+ | |||
+ | ==Solution 2== | ||
+ | <math>292,526,838</math> miles is extremely close to <math>300,000,000</math> miles. We also know that <math>6.5</math> months is equivalent to <math>6.5\cdot30\cdot24</math> hours. Now, we can calculate the speed in miles per hour, which we find is about <math>\boxed{\textbf{(C) }60,000}</math>. | ||
+ | |||
+ | <cmath>\dfrac{300000000}{6.5\cdot30\cdot24}=\dfrac{10000000}{6.5\cdot24}\\ | ||
+ | =\dfrac{10000000}{13\cdot12}\\ | ||
+ | =\dfrac{10000000}{156}\\ | ||
+ | \approx\dfrac{10000000}{150}\\ | ||
+ | \approx\dfrac{200000}{3}\\ | ||
+ | \approx60000</cmath> | ||
+ | |||
+ | ~MathFun1000 | ||
==Animated Video Solution== | ==Animated Video Solution== |
Revision as of 23:04, 24 January 2023
Solution 1
Since the answers are so far apart, we just need to compute the # of figures the answer contains. So by approximating all the values for the hourly rate we have which is
~apex304
Solution 2
miles is extremely close to
miles. We also know that
months is equivalent to
hours. Now, we can calculate the speed in miles per hour, which we find is about
.
~MathFun1000
Animated Video Solution
~Star League (https://starleague.us)