AMC 8 · 2016 · #1
Easy mode Grade 4Problem
The longest professional tennis match ever played lasted 11 hours and 5 minutes.
Picture the whole match laid out as one long stretch of time. We want to know its length in minutes only.
How many minutes long was the match?
Pick an answer.
AMC 8 2016 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: A tennis match lasted $11$ hours and $5$ minutes. Express that total duration entirely in minutes.
Givens: Match duration: $11$ hours and $5$ minutes; Standard conversion: $1$ hour $= 60$ minutes; Answer choices: (A) $605$, (B) $655$, (C) $665$, (D) $1005$, (E) $1105$
Unknowns: The total duration written as a single number of minutes
Understand
Restated: A tennis match lasted $11$ hours and $5$ minutes. Express that total duration entirely in minutes.
Givens: Match duration: $11$ hours and $5$ minutes; Standard conversion: $1$ hour $= 60$ minutes; Answer choices: (A) $605$, (B) $655$, (C) $665$, (D) $1005$, (E) $1105$
Plan
Primary tool: #8 Analyze the Units
Secondary: #7 Identify Subproblems
The problem mixes two time units (hours and minutes) and asks for a single unit (minutes). Tool #8 (Analyze the Units) is the natural fit: convert hours to minutes using the rate $60 \tfrac{\text{min}}{\text{hr}}$ so every quantity is in the same unit before adding. Tool #7 (Identify Subproblems) is the matching habit — split the total into "minutes coming from the $11$ hours" and "the extra $5$ minutes", solve each, then combine.
Execute — Answer: C
4.MD.A.2 Step 1 - Split the duration into two pieces: the $11$-hour part and the leftover $5$-minute part.
- Convert each to minutes separately, then add.
💡 Solving "hours $\to$ minutes" and "add the leftover minutes" as two clean subproblems is the Tool #7 move.
4.MD.A.1 Step 2 - Convert $11$ hours into minutes.
- Since $1$ hour $= 60$ minutes, multiply: $11 \times 60$.
- The unit ratio $60 \tfrac{\text{min}}{\text{hr}}$ cancels "hours" and leaves "minutes".
💡 Tracking units lets you see that hours $\times$ (min/hr) gives minutes, the unit the question wants.
4.NBT.B.4 Step 3 - Add the leftover $5$ minutes to the $660$ minutes from the hours part.
- Both addends are now in minutes, so the sum is the total duration in minutes.
💡 Once units match, adding is straightforward whole-number addition.
4.MD.A.2 Split the duration into two pieces: the $11$-hour part and the leftover $5$-minu 4.MD.A.1 Convert $11$ hours into minutes. Since $1$ hour $= 60$ minutes, multiply: $11 \t 4.NBT.B.4 Add the leftover $5$ minutes to the $660$ minutes from the hours part. Both adde Review
Reasonableness: An hour is $60$ minutes, so $11$ hours alone should be a bit over $600$ minutes. $11 \times 60 = 660$ is in that range, and adding the small extra $5$ minutes gives $665$ — clearly between (A) $605$ and (D) $1005$. Choice (A) $605$ would be the trap if you accidentally used $55$ instead of $60$ minutes per hour ($11 \times 55 = 605$). Choice (E) $1105$ is what you get from concatenating the digits "$11$" and "$05$" instead of computing — a written-form trap. $665$ is the only value consistent with the actual minute-per-hour rate.
Alternative: Tool #3 (Eliminate Possibilities) on the choices: each option divided by $60$ should give back roughly $11$ hours plus a small remainder. $665 \div 60 = 11$ remainder $5$ — matches exactly. $605 \div 60 = 10$ remainder $5$ (only $10$ hours, wrong). $655 \div 60 = 10$ remainder $55$. $1005 \div 60 = 16$ remainder $45$. $1105 \div 60 = 18$ remainder $25$. Only (C) recovers $11$ hours $5$ minutes, confirming the answer.
CCSS standards used (min grade 4)
4.MD.A.2Solve word problems involving distances, time, liquid volumes, and money (Framing the problem as a Grade 4 time word-problem: split a mixed-unit duration into an hours part and a minutes part.)4.MD.A.1Know relative sizes of measurement units and convert larger to smaller units (Converting $11$ hours to $11 \times 60 = 660$ minutes using the relationship $1$ hour $= 60$ minutes.)4.NBT.B.4Fluently add and subtract multi-digit whole numbers (Adding $660 + 5 = 665$ to combine the two minute-quantities into the final total.)
⭐ This AMC 8 problem only needs Grade 4 unit conversion — once you turn hours into minutes, it's just addition.
⭐ This AMC 8 problem only needs Grade 4 unit conversion — once you turn hours into minutes, it's just addition.
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