🇺🇸 AMC 8 ⇄ switch contest
2012 AMC 8

Problem 3

Problem 3 · 2012 AMC 8 Easy
Arithmetic & Operations time-arithmetic

On February 13 The Oshkosh Northwester listed the length of daylight as 10 hours and 24 minutes, the sunrise was 6:57 AM, and the sunset as 8:15 PM. The length of daylight and sunrise were correct, but the sunset was wrong. When did the sun really set?

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Answer: B — 5:21 PM.
Show hints
Hint 1 of 2
The wrong sunset (8:15 PM) is a trap — ignore it completely. Daylight is just the gap between sunrise and sunset, so sunset = sunrise + daylight.
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Hint 2 of 2
Add time in two clean stages: whole hours first, then the leftover minutes. Adding 10 h 24 min all at once invites a carrying mistake.
Show solution
Approach: sunset = sunrise + daylight, added in stages
  1. Daylight is the stretch from sunrise to sunset, so just add 10 h 24 min to the 6:57 AM sunrise (the listed 8:15 PM is a decoy).
  2. Add the 10 whole hours first: 6:57 AM + 10 h lands at 4:57 PM.
  3. Now add the 24 minutes: 4:57 + 24 min = 5:21 PM.
  4. Splitting hours from minutes is the reusable trick for any clock arithmetic — it keeps the carry into the next hour easy to see.
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