Problem 3 · 2006 AMC 8
Easy
Ratios, Rates & Proportions
minutes-per-lap
Elisa swims laps in the pool. When she first started, she completed 10 laps in 25 minutes. Now she can finish 12 laps in 24 minutes. By how many minutes has she improved her lap time?
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Answer: A — 1/2 minute.
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Hint 1 of 2
The question asks about her lap time — how long ONE lap takes. So convert each situation to minutes-per-lap before comparing; don't compare 25 vs 24 directly.
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Hint 2 of 2
"Per one lap" means divide minutes by laps. The unit you want (min/lap) tells you which number goes on top.
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Approach: convert each to minutes per lap, then subtract
- Lap time = total minutes ÷ number of laps. Before: 25 ÷ 10 = 2.5 min/lap. Now: 24 ÷ 12 = 2 min/lap.
- She shaved off 2.5 − 2 = 1/2 minute per lap.
- Why convert first: the two situations use different lap counts, so the totals (25 and 24) aren't comparable. Reducing both to the same per-unit measure makes them line up — this "put everything in the same units" move powers almost every rate problem.
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