Competition · AMC preparation · step 4 of 4
AMC 8 · 2012 · #3
Grade 4 arithmeticPick an answer.
AMC 8 2012 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.
Sunset = sunrise + daylight is a single sum, but it is cleaner to split it into two subproblems (Tool #7): add the hours, then add the minutes, then carry. After computing, Tool #3 (Eliminate Possibilities) lets us check the answer against the five choices — a free verification on any AMC multiple-choice problem. Tool #8 (Units) is implicitly used, but the bookkeeping here is hours vs. minutes, not a unit conversion across systems, so #7 captures the structure best.
Set up the time sum
Daylight runs from sunrise to sunset, so the correct sunset equals sunrise plus the daylight length; ignore the misprinted one.
Picking the right relationship before computing is the first move of Tool #7 — name the subproblems before doing them.
The correct sunset time equals the correct sunrise time plus the length of daylight.
▸ Why?
Daylight names the single stretch of time that runs from sunrise to sunset, so the true sunset is the moment you reach by starting at sunrise and letting all of that daylight pass; the wrongly printed sunset plays no part.
▸ Why?
That daylight stretch fills the span from sunrise to sunset exactly, with no minute left out and none counted twice, so sunrise together with the whole daylight length accounts for the entire way to sunset.
▸ Why?
Calling daylight that span means daylight equals sunset minus sunrise, and adding the daylight back onto sunrise recovers sunset because adding reverses that same subtraction.
Add the hours
Add the hours: 6 (from 6{:}57) plus 10 hours of daylight gives 16 hours.
Treating hours as their own column is exactly the "add place by place" Grade 4 algorithm.
4.NBT.B.4Identify SubproblemsAdd the minutes
Add the minutes: 57 plus 24 gives 81 minutes.
Same place-value addition, this time in the minutes column.
4.NBT.B.4Identify SubproblemsCarry 60 minutes into an hour
81 minutes tops 60, so trade 60 for 1 hour: 21 minutes are left and the hours climb to 17, giving 17 h 21 min.
Trading 60 minutes for 1 hour is the same idea as carrying 10 ones into a ten — Grade 4 unit conversion within the time system.
4.MD.A.1Identify SubproblemsConvert to PM time
Subtract 12 from the hours: 17{:}21 becomes 5{:}21 PM, which is choice (B).
Matching the computed result against the five choices is Tool #3 (Eliminate Possibilities) — only (B) survives, the rest are off by 11, 20, 36, or 42 minutes.
4.MD.A.2Eliminate PossibilitiesIf you can add hours, add minutes, and carry 60 minutes as 1 hour, you have all the Grade 4 skills this AMC 8 problem needs.
- Set up the time sum
- Add the hours
- Add the minutes
- Carry 60 minutes into an hour
- Convert to PM time
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