Problem 6 · 2002 AMC 8
Medium
Ratios, Rates & Proportions
unit-rategraph-reading
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Answer: A — Graph A — the volume rises steadily, then stays constant once the bath overflows.
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Hint 1 of 2
Don't match numbers — match the *story shape*. The bath has two chapters: filling up, then full-and-overflowing. Picture each chapter's slope.
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Hint 2 of 2
While filling, the net gain (in minus out) is the *same* every minute, so the line is straight and rising. Once it overflows, what goes in spills out, so the amount inside stops changing — flat.
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Approach: net inflow until full, then constant
- Read the graph from the story, not the arithmetic. Chapter 1: water arrives faster than it leaves, by a *constant* 20 − 18 = 2 mL each minute. A constant rate of change means a *straight line* tilting up.
- Chapter 2: the bath is full and overflowing — every mL in is a mL out, so the volume inside holds steady: a *flat* line.
- A straight rise that then levels off is graph A.
- *The transferable skill:* turn a rate story into a graph by reading its *slopes*. Constant rate → straight segment; no change → flat segment; faster/slower → steeper/shallower. You never need exact values to pick the right shape.
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