AMC 8 · 2016 · #1

Grade 4 arithmetic

Archetype Arithmetic Expression Decomposition

unit-conversionmulti-digit-arithmetic dimensional-analysisidentify-subproblems ↑ Prerequisites: multi-digit-arithmetic

📏 Short solution 💡 2 insights

Problem

The longest professional tennis match ever played lasted a total of $11$ hours and $5$ minutes. How many minutes was this?

$\textbf{(A) }605\qquad\textbf{(B) }655\qquad\textbf{(C) }665\qquad\textbf{(D) }1005\qquad \textbf{(E) }1105$

Pick an answer.

(A)

605

(B)

655

(C)

665

(D)

1005

(E)

1105

View mode:

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

#7 Identify Subproblems 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.

$$11 \text{ hr} + 5 \text{ min} \;\longrightarrow\; (\text{minutes from } 11 \text{ hr}) + 5 \text{ min}$$

💡 Solving "hours $\to$ minutes" and "add the leftover minutes" as two clean subproblems is the Tool #7 move.

#8 Analyze the Units 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".

$$11 \text{ hr} \times 60 \tfrac{\text{min}}{\text{hr}} = 660 \text{ min}$$

💡 Tracking units lets you see that hours $\times$ (min/hr) gives minutes, the unit the question wants.

#8 Analyze the Units 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.

$$660 \text{ min} + 5 \text{ min} = 665 \text{ min} \;\Rightarrow\; \textbf{(C)}$$

💡 Once units match, adding is straightforward whole-number addition.

[1] #7 4.MD.A.2 Split the duration into two pieces: the $11$-hour part and the leftover $5$-minu

[2] #8 4.MD.A.1 Convert $11$ hours into minutes. Since $1$ hour $= 60$ minutes, multiply: $11 \t

[3] #8 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.2 Solve 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.1 Know 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.4 Fluently 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.

Problem

Toolkit + CCSS Solution

Understand

Plan

Execute — Answer: C

Review

CCSS standards used (min grade 4)

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