Problem 19 · 2001 AMC 8
Hard
Ratios, Rates & Proportions
distance-speed-timegraph-reading
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Answer: D — Graph D.
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Hint 1 of 2
On a speed-vs-time graph, the distance traveled is the AREA of the rectangle under the line (speed × time). Both cars cover the same distance, so both rectangles have the same area.
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Hint 2 of 2
Double the height (speed) with the same area forces half the width (time) — so look for N's line drawn twice as high but half as long as M's.
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Approach: twice the speed over the same distance halves the time
- Read the axes: speed is vertical, time horizontal, and a constant speed is a horizontal line. Distance = speed × time = the area under that line.
- Car N is twice as fast, so its line sits at twice M's height. Same distance means same area, so doubling the height must halve the width — N's line runs only half as long in time.
- The graph with N higher AND shorter than M is D. The takeaway: on speed-time graphs, area = distance, so trading height for width keeps distance fixed.
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