AMC 8 · 2012 · #3
Easy mode Grade 4Problem
On February 13, the sun came up at 6:57\textscam. That day, the sun was up for 10 hours and 24 minutes.
The newspaper printed a sunset time of 8:15\textscpm, but that was wrong. The sunrise time and the length of daylight were both correct.
What time did the sun actually set?
Pick an answer.
AMC 8 2012 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.
Try it yourself first — the explanation is most useful after you’ve attempted it.
Toolkit + CCSS Solution
Understand
Restated: On February 13, the newspaper reports daylight as $10$ hours $24$ minutes, sunrise at $6{:}57$ AM, and sunset at $8{:}15$ PM. The daylight length and sunrise are correct, but the printed sunset is wrong. Find the actual sunset time.
Givens: Sunrise time: $6{:}57$ AM (correct); Length of daylight: $10$ hours $24$ minutes (correct); Printed sunset: $8{:}15$ PM (wrong — ignore); Answer choices: (A) $5{:}10$ PM, (B) $5{:}21$ PM, (C) $5{:}41$ PM, (D) $5{:}57$ PM, (E) $6{:}03$ PM
Unknowns: The correct sunset time, written in $12$-hour PM format
Understand
Restated: On February 13, the newspaper reports daylight as $10$ hours $24$ minutes, sunrise at $6{:}57$ AM, and sunset at $8{:}15$ PM. The daylight length and sunrise are correct, but the printed sunset is wrong. Find the actual sunset time.
Givens: Sunrise time: $6{:}57$ AM (correct); Length of daylight: $10$ hours $24$ minutes (correct); Printed sunset: $8{:}15$ PM (wrong — ignore); Answer choices: (A) $5{:}10$ PM, (B) $5{:}21$ PM, (C) $5{:}41$ PM, (D) $5{:}57$ PM, (E) $6{:}03$ PM
Plan
Primary tool: #7 Identify Subproblems
Secondary: #3 Eliminate Possibilities
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.
Execute — Answer: B
4.MD.A.2 Step 1 - Set up the relationship.
- Daylight is the time from sunrise to sunset, so the correct sunset equals the correct sunrise plus the correct daylight length.
- Ignore the printed (wrong) sunset.
💡 Picking the right relationship before computing is the first move of Tool #7 — name the subproblems before doing them.
4.NBT.B.4 Step 2 - Subproblem 1: add the hours.
- $6$ hours (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.4 Step 3 - Subproblem 2: add the minutes.
- $57$ minutes plus $24$ minutes is $81$ minutes.
💡 Same place-value addition, this time in the minutes column.
4.MD.A.1 Step 4 - Carry.
- $81$ minutes is more than $60$, so peel off $60$ minutes as $1$ hour.
- That leaves $21$ minutes and bumps the hour count from $16$ to $17$.
💡 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.2 Step 5 - Convert $17{:}21$ in $24$-hour format to PM time by subtracting $12$ from the hours.
- Then check the answer choices: $5{:}21$ PM 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.2 Set up the relationship. Daylight is the time from sunrise to sunset, so the cor 4.NBT.B.4 Subproblem 1: add the hours. $6$ hours (from $6{:}57$) plus $10$ hours of daylig 4.NBT.B.4 Subproblem 2: add the minutes. $57$ minutes plus $24$ minutes is $81$ minutes. 4.MD.A.1 Carry. $81$ minutes is more than $60$, so peel off $60$ minutes as $1$ hour. Tha 4.MD.A.2 Convert $17{:}21$ in $24$-hour format to PM time by subtracting $12$ from the ho Review
Reasonableness: Quick sanity check: $10$ hours $24$ minutes after $6{:}57$ AM should land in the late afternoon. Round to $11$ hours after $7$ AM, that is roughly $6$ PM, so a sunset near $5$ to $6$ PM is plausible. The exact value $5{:}21$ PM sits in that window. Reverse-check: from $5{:}21$ PM back to $6{:}57$ AM, count from $6{:}57$ AM to $5{:}21$ PM as $5$ hours $3$ minutes to noon, plus $5$ hours $21$ minutes after noon, totaling $10$ hours $24$ minutes. Matches.
Alternative: Tool #11 (Work Backwards): start from each PM choice, subtract $10$ h $24$ min, and see which one gives $6{:}57$ AM. $5{:}21$ PM $-$ $10$ h $24$ min $=$ $6{:}57$ AM exactly, picking out (B). The other choices land at $6{:}46$, $7{:}17$, $7{:}33$, or $7{:}39$ AM — none match the given sunrise.
CCSS standards used (min grade 4)
4.MD.A.2Solve word problems involving distances, time, liquid volumes, and money (Recognizing that sunset = sunrise + daylight and computing the elapsed-time word problem in hours and minutes.)4.NBT.B.4Fluently add and subtract multi-digit whole numbers using the standard algorithm (Adding the hours ($6 + 10 = 16$) and the minutes ($57 + 24 = 81$) column by column before regrouping.)4.MD.A.1Know relative sizes of measurement units within one system; convert larger units to smaller (Trading $60$ minutes for $1$ hour to rewrite $16$ h $81$ min as $17$ h $21$ min, and converting $17{:}21$ from $24$-hour to $12$-hour PM format.)
⭐ If 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.
⭐ If 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.
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