2006 AMC 8 Problem 3

Attempt Problem 3 of the 2006 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2006 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

3.

Elisa swims laps in the pool. When she first started, she completed 1010 laps in 2525 minutes. Now, she can finish 1212 laps in 2424 minutes. By how many minutes has she improved her lap time?
12\dfrac{1}{2}
34\dfrac{3}{4}
11
22
33
Answer: A
Concepts:rate
Small hint:
Find Elisa’s minutes per lap before and after the improvement.
Big hint:
Compare 2510\frac{25}{10} minutes per lap with 2412\frac{24}{12} minutes per lap.
Solution:
Initially, Elisa swam one lap in 2510=2.5\frac{25}{10}=2.5 minutes. Now she swims one lap in 2412=2\frac{24}{12}=2 minutes.
Therefore, she improved her lap time by 2.5−2=0.5=122.5-2=0.5=\dfrac{1}{2} minute.
Thus, A is the correct answer.
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