Problem 23 · 1990 AJHSME
Hard
Ratios, Rates & Proportions
read-graphslope
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Answer: B — The second hour (1-2).
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Hint 1 of 2
Speed = distance ÷ time, and every choice covers the same one hour. So 'fastest hour' just means 'the hour where the distance climbed the most' — you're comparing rises, not doing division.
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Hint 2 of 2
On a distance–time graph, the steeper the line over an hour, the faster the plane went that hour. Don't read exact numbers — just eyeball where the curve shoots up most sharply.
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Approach: steepest one-hour segment = fastest hour (read the slope by eye)
- Average speed over an hour = (miles gained) ÷ (1 hour) = the miles gained that hour. Since every option is a 1-hour stretch, the fastest hour is simply the one with the biggest jump in distance — the steepest part of the graph.
- Scan the curve: between hours 1 and 2 it leaps from about 400 to about 900 miles — roughly a 500-mile climb, clearly steeper than any other single hour (the later hours flatten out).
- So the largest average speed is during the second hour (1-2).
- *Worth keeping:* on a distance–time graph, steepness *is* speed — comparing slopes by eye beats computing every segment, and a flattening curve means slowing down.
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