Problem 3 · 2009 AMC 8
Easy
Ratios, Rates & Proportions
unit-rate
The graph shows the constant rate at which Suzanna rides her bike. If she rides a total of a half an hour at the same speed, how many miles would she have ridden?
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Answer: C — 6 miles.
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Hint 1 of 2
"Constant rate" is the key phrase: one dot on the graph fixes the speed forever, so you don't need the line to reach 30 minutes — you can just scale up.
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Hint 2 of 2
Read one easy point off the graph, turn it into a simple per-minute rate, then count how many of those time-chunks fit in 30 minutes.
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Approach: read one point, scale to the new time
- Pick the cleanest point on the line: she goes 1 mile every 5 minutes.
- Half an hour = 30 minutes, which is 30 ÷ 5 = 6 of those 5-minute chunks. So 6 × 1 = 6 miles.
- Why this works: a straight line through the origin means distance and time grow in lockstep — one ratio (1 mile / 5 min) describes every point, so rescaling is all you ever need.
Another way — unit rate then multiply:
- Speed = 1 mile / 5 min = 0.2 mi/min, which is 12 mph.
- In 0.5 hour: 12 × 0.5 = 6 miles.
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