Problem 9 · 2011 AMC 8
Easy
Ratios, Rates & Proportions
average-speed
Carmen takes a long bike ride on a hilly highway. The graph indicates the miles traveled during the time of her ride. What is Carmen's average speed for her entire ride in miles per hour?
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Answer: E — 5 mph.
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Hint 1 of 2
Average speed doesn't care about the hills, the slow stretches, or the bends in the graph — only where the ride started and where it ended. Read just the final point.
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Hint 2 of 2
Average speed = total distance ÷ total time. The far-right end of the curve gives you both at once.
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Approach: average speed depends only on the endpoints
- The curve ends at 35 miles after 7 hours — that's the whole ride: 35 miles in 7 hours.
- Average speed = total distance ÷ total time = 35 ÷ 7 = 5 mph.
- Why this transfers: "average speed" is always end-distance over end-time. The wiggly middle of a distance-time graph is a distraction — never average the steeper and flatter parts.
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