2012 AMC 8 Problem 3

Attempt Problem 3 of the 2012 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 2012 AMC 8 solutions, or check the answer key.

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

3.

On February 1313 The Oshkosh Northwester listed the length of daylight as 1010 hours and 2424 minutes, the sunrise as 6:57 AM,6:57\text{ AM}, and the sunset as 8:15PM. 8:15\text{PM} . The length of daylight and sunrise were correct, but the sunset was wrong. When did the sun really set?
5 5:10 PM10\text{ PM}
55:21 PM21\text{ PM}
5 5:41 PM41\text{ PM}
5 5:57 PM57\text{ PM}
6 6:03 PM03\text{ PM}
Answer: B
Concepts:date and time
Small hint:
Add the correct daylight length to the sunrise time.
Big hint:
From 6:576:57 AM to noon is 55 hours 33 minutes.
Video solution:
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Written solution:
Since 1010 hours after 6:57AM6:57 \text{AM} is 4:57PM,4:57 \text{PM} , we can then say 1010 hours and 33 minutes after sunrise is 5:00PM.5:00 \text{PM} . We then have 2121 more minutes until sunset, so sunset is 5:21PM.5:21 \text{PM} .
Thus, the answer is B .
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