1994 AMC 8 Problem 18
Attempt Problem 18 of the 1994 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 1994 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
18.
Mike leaves home and drives slowly east through city traffic. When he reaches the highway he drives east more rapidly until he reaches the shopping mall where he stops. He shops at the mall for an hour. Mike returns home by the same route as he came, driving west rapidly along the highway and then slowly through city traffic. Each graph shows the distance from home on the vertical axis versus the time elapsed since leaving home on the horizontal axis. Which graph is the best representation of Mike’s trip?
Answer: B
Small hint:
Distance from home increases on the way out, stays constant during the hour of shopping, and decreases on the way back.
Big hint:
Slow city driving is a gentle (shallow) slope and fast highway driving is a steep slope; the stop at the mall is a flat, horizontal segment.
Solution:
On the way out Mike drives slowly (a shallow slope) then rapidly (a steep slope), so the distance rises slowly and then more steeply. During the hour at the mall the distance stays the same, a flat segment.
On the return he drives rapidly (steep) then slowly (shallow), so the distance falls steeply and then more gently. Only the graph with a slow-then-fast rise, a flat top, and a fast-then-slow fall fits.
Thus, the correct answer is B .
Problem 18 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
- 1992 AMC 8
- 1993 AMC 8
- 1995 AMC 8
- 1996 AMC 8
- 1997 AMC 8
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- 1999 AMC 8
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