Problem 9 · 2023 AMC 8
Medium
Algebra & Patterns
evaluate-formula
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Answer: B — 8 seconds.
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Hint 1 of 2
You don't care how high she is — only when she's inside the 4-to-7 band. Think of it as a horizontal stripe on the graph.
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Hint 2 of 2
Draw horizontal lines at 4 and 7; the curve enters and leaves that stripe a few times. Add up how long it stays inside each time.
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Approach: read the graph between two horizontal lines
- Re-frame the question as a horizontal stripe: shade the band between elevation 4 and 7. The answer is just how much time (horizontal distance) the curve spends inside that band — her actual height inside it is irrelevant.
- The curve dips into and out of the band three times: roughly t = 2 to 4 (2 sec), t = 6 to 10 (4 sec), and t = 12 to 14 (2 sec).
- Total: 2 + 4 + 2 = 8 seconds. This transfers: ‘how long is the value between A and B’ on any graph means ‘sum the horizontal widths where the curve lies between two horizontal lines.’
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