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.) |
MRENTHUSIASM (talk | contribs) m (→Solution 2) |
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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), his average speed during the entire trip was the average of the speeds <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 \\ |
Revision as of 13:00, 18 September 2021
- The following problem is from both the 2018 AMC 12B #2 and 2018 AMC 10B #2, so both problems redirect to this page.
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), his average speed during the entire trip was the average of the speeds
mph,
mph, and
mph. We have
~coolmath_2018 (Solution)
~MRENTHUSIASM (Minor Edits)
Video Solution
~savannahsolver
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.