Difference between revisions of "2018 AMC 10B Problems/Problem 2"
MRENTHUSIASM (talk | contribs) (Made Sol 1 considerably more concise. Also, corrected typos in Sol 2 as well as mentioning an underlying assumption.) |
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Suppose that Sam's average speed during the last <math>30</math> minutes was <math>x</math> mph. | Suppose that Sam's average speed during the last <math>30</math> minutes was <math>x</math> mph. | ||
| − | Note that Sam's average speed during the entire trip was <math>\frac{96}{3/2}=64</math> mph. Since Sam drove at <math>60</math> mph, <math>65</math> mph, and <math>x</math> mph for the same | + | Note that Sam's average speed during the entire trip was <math>\frac{96}{3/2}=64</math> mph. Since Sam drove at <math>60</math> mph, <math>65</math> mph, and <math>x</math> mph for the same duration (<math>30</math> minutes each), his average speed during the entire trip was the average of <math>60</math> mph, <math>65</math> mph, and <math>x</math> mph. We have |
<cmath>\begin{align*} | <cmath>\begin{align*} | ||
\frac{60+65+x}{3}&=64 \\ | \frac{60+65+x}{3}&=64 \\ | ||
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x&=\boxed{\textbf{(D) } 67}. | x&=\boxed{\textbf{(D) } 67}. | ||
\end{align*}</cmath> | \end{align*}</cmath> | ||
| − | ~coolmath_2018 | + | ~coolmath_2018 ~MRENTHUSIASM |
| − | |||
| − | ~MRENTHUSIASM | ||
== Video Solution == | == Video Solution == | ||
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~savannahsolver | ~savannahsolver | ||
| + | |||
| + | ==Video Solution (HOW TO THINK CRITICALLY!!!)== | ||
| + | https://youtu.be/VN88m4xUHM0 | ||
| + | |||
| + | ~Education, the Study of Everything | ||
==See Also== | ==See Also== | ||
Latest revision as of 01:37, 28 May 2023
- The following problem is from both the 2018 AMC 12B #2 and 2018 AMC 10B #2, so both problems redirect to this page.
Contents
Problem
Sam drove 
miles in 
minutes. His average speed during the first 
minutes was 
mph (miles per hour), and his average speed during the second minutes was 
mph. What was his average speed, in mph, during the last minutes?
Solution 1
Suppose that Sam's average speed during the last minutes was 
mph.
Recall that a half hour is equal to minutes. Therefore, Sam drove 
miles during the first half hour, 
miles during the second half hour, and 
miles during the last half hour. We have 
~Haha0201 ~MRENTHUSIASM
Solution 2
Suppose that Sam's average speed during the last minutes was mph.
Note that Sam's average speed during the entire trip was 
mph. Since Sam drove at mph, mph, and mph for the same duration ( minutes each), his average speed during the entire trip was the average of mph, mph, and mph. We have
~coolmath_2018 ~MRENTHUSIASM
Video Solution
~savannahsolver
Video Solution (HOW TO THINK CRITICALLY!!!)
~Education, the Study of Everything
See Also
| 2018 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 1 |
Followed by Problem 3 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AMC 10 Problems and Solutions | ||
| 2018 AMC 12B (Problems • Answer Key • Resources) | |
| Preceded by Problem 1 |
Followed by Problem 3 |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
