1990 AMC 8 Problem 23
Attempt Problem 23 of the 1990 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1990 AMC 8 solutions, or check the answer key.
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23.
The graph relates the distance traveled (in miles) to the time elapsed (in hours) on a trip taken by an experimental airplane. During which hour was the average speed of this airplane the largest?
first
second
third
ninth
last
Answer: B
Small hint:
The average speed during an hour equals the distance covered in that hour, which is how far the curve climbs from the start of the hour to its end
Big hint:
Find the one-hour interval over which the graph rises the most steeply
Solution:
The average speed during any single hour equals the distance the airplane covers in that hour, which on the graph is the vertical rise of the curve over that one-hour interval. So the largest average speed happens during the hour where the curve is steepest.
From to the curve climbs from about miles to about miles, a rise of roughly miles, giving an average speed near mph. During every other hour the curve rises by less than miles, so those average speeds are all smaller. The steepest climb, and hence the largest average speed, is during the second hour.
Thus, the correct answer is B .
Problem 23 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
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- 1989 AMC 8
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