Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Difference between revisions of "2023 AMC 8 Problems/Problem 11"
Line 1: Line 1:
−
==Written Solution==
+
==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 22:04, 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 $\frac{300,000,000}{5 * 30 * 30} \approx \frac{300,000,000}{5000} = 60,000$ which is $\boxed{\text{(C)}60,000}$

~apex304

Solution 2

$292,526,838$ miles is extremely close to $300,000,000$ miles. We also know that $6.5$ months is equivalent to $6.5\cdot30\cdot24$ hours. Now, we can calculate the speed in miles per hour, which we find is about $\boxed{\textbf{(C) }60,000}$.

\[\dfrac{300000000}{6.5\cdot30\cdot24}=\dfrac{10000000}{6.5\cdot24}\\ =\dfrac{10000000}{13\cdot12}\\ =\dfrac{10000000}{156}\\ \approx\dfrac{10000000}{150}\\ \approx\dfrac{200000}{3}\\ \approx60000\]

~MathFun1000

Animated Video Solution

https://youtu.be/hwR2VM9tHJ0

~Star League (https://starleague.us)

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2023_AMC_8_Problems/Problem_11&oldid=187679"