Difference between revisions of "2023 AMC 8 Problems/Problem 11"
Mathfun1000 (talk | contribs) |
Mathfun1000 (talk | contribs) m |
||
| Line 7: | Line 7: | ||
<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>. | <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{ | + | <cmath>\dfrac{300,000,000}{6.5\cdot30\cdot24}=\dfrac{10,000,000}{6.5\cdot24}\\ |
| − | =\dfrac{ | + | =\dfrac{10,000,000}{13\cdot12}\\ |
| − | =\dfrac{ | + | =\dfrac{10,000,000}{156}\\ |
| − | \approx\dfrac{ | + | \approx\dfrac{10,000,000}{150}\\ |
| − | \approx\dfrac{ | + | \approx\dfrac{200,000}{3}\\ |
| − | \ | + | \approx60,000</cmath> |
~MathFun1000 | ~MathFun1000 | ||
Revision as of 22:05, 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 
.
![\[\dfrac{300,000,000}{6.5\cdot30\cdot24}=\dfrac{10,000,000}{6.5\cdot24}\\ =\dfrac{10,000,000}{13\cdot12}\\ =\dfrac{10,000,000}{156}\\ \approx\dfrac{10,000,000}{150}\\ \approx\dfrac{200,000}{3}\\ \approx60,000\]](http://latex.artofproblemsolving.com/d/1/1/d111dcd3ef78b74946385e5118a61764c56702b5.png)
~MathFun1000
Animated Video Solution
~Star League (https://starleague.us)
