2018 AMC 10B Problems/Problem 2
- 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?
Solutions
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 . ~coolmath_2018
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.