Difference between revisions of "2018 AMC 10B Problems/Problem 2"
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− | ==Solution== | + | ==Solution 1 == |
Let Sam drive at exactly <math>60</math> mph in the first half hour, <math>65</math> mph in the second half hour, and <math>x</math> mph in the third half hour. | Let Sam drive at exactly <math>60</math> mph in the first half hour, <math>65</math> mph in the second half hour, and <math>x</math> mph in the third half hour. | ||
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Therefore, Sam was driving <math>\boxed{\textbf{(D) } 67}</math> miles per hour in the third half hour. | Therefore, Sam was driving <math>\boxed{\textbf{(D) } 67}</math> miles per hour in the third half hour. | ||
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+ | ==Solution 2 (Faster)== | ||
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+ | The average speed for the total trip is <cmath>\text{avg. speed} = \frac{96}{\frac{3}{2}} = 64.</cmath> Therefore the average speed for the total trip is the average of the average speeds of the three intrevals. So we have <math>64 = \frac{60 + 65 + x}{3}</math> and solving for <math>x = 67</math>. So the answer is <math>\boxed{\textbf{(D) } 67}</math>. | ||
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==Video Solution== | ==Video Solution== |
Revision as of 22:24, 26 November 2020
Problem
Sam drove 96 miles in 90 minutes. His average speed during the first 30 minutes was 60 mph (miles per hour), and his average speed during the second 30 minutes was 65 mph. What was his average speed, in mph, during the last 30 minutes?
Solution 1
Let Sam drive at exactly mph in the first half hour, mph in the second half hour, and mph in the third half hour.
Due to , and that min is half an hour, he covered miles in the first mins.
SImilarly, he covered miles in the nd half hour period.
The problem states that Sam drove miles in min, so that means that he must have covered miles in the third half hour period.
, so .
Therefore, Sam was driving miles per hour in the third half hour.
Solution 2 (Faster)
The average speed for the total trip is Therefore the average speed for the total trip is the average of the average speeds of the three intrevals. So we have and solving for . So the answer is .
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 |
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