2016 AMC 8 Problem 4

Attempt Problem 4 of the 2016 AMC 8 below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2016 AMC 8 solutions, or check the answer key.

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

4.

When Cheenu was a boy he could run 1515 miles in 33 hours and 3030 minutes. As an old man he can now walk 1010 miles in 44 hours. How many minutes longer does it take for him to walk a mile now compared to when he was a boy?
6 6
10 10
15 15
18 18
30 30
Answer: B
Concepts:rateunit conversion
Small hint:
Compare the two paces in minutes per mile.
Big hint:
Convert 33 hours 3030 minutes to minutes before dividing by 1515.
Video solution:
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Written solution:
To better compare the rates, we can change his speed into minutes per mile.
As a boy he ran 1515 miles in 3⋅60+30=2103 \cdot 60 + 30 = 210 minutes, which means that he ran at a pace of 21015=14\frac{210}{15} = 14 minutes per mile.
As an adult, he can walk 1010 miles in 4⋅60=2404 \cdot 60 = 240 minutes, which means he walks at a pace of 24010=24\frac{240}{10} = 24 minutes per mile.
Subtracting the two, we get that he takes 1010 more minutes to walk a mile as an adult.
Thus, B is the correct answer.
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