AMC 8 · 2001 · #1

Grade 4 arithmeticrate-ratio
Archetype Arithmetic Expression Decomposition └ Sub-archetype Linear Rate Accumulation
rateunit-conversionmulti-digit-arithmetic identify-subproblemsdimensional-analysis ↑ Prerequisites: multi-digit-arithmetic
📏 Short solution 💡 2 insights
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Problem
Casey paints 300 dimples on a golf ball. Each dimple takes 2 seconds to paint. How many minutes does the whole job take?

Pick an answer.

(A)
4
(B)
6
(C)
8
(D)
10
(E)
12

AMC 8 2001 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.

How to solve
Strategy Break into Subproblems

The question mixes two ideas: how long the painting takes, and what unit the answer should be in. Tool #7 (Break into Subproblems) splits the work into two clean steps — first find the total time in seconds, then deal with the unit. Tool #16 (Change Representation) handles the second step: rewriting a seconds total as minutes by dividing by 60. Keeping the two steps separate prevents unit-mixing mistakes.

1STEP 1

Total time in seconds: 300 dimples times 2 seconds each gives 600 seconds.

300 × 2 = 600 seconds
2STEP 2

Convert seconds to minutes: divide 600 by 60 to get 10 minutes.

600 ÷ 60 = 10 minutes
3STEP 3

Match the result to the choices: 10 minutes is choice (D).

10 minutes → (D)
Answer
10
Quick sanity check by working backward: 10 minutes is 10 × 60 = 600 seconds, and 600 ÷ 2 = 300 dimples. That matches the problem exactly. Also, the size feels right: 2 seconds per dimple is fast, so painting hundreds of them should still finish in only a few minutes, not hours.
💡Key takeaway

When a problem mixes amounts and units, do them in order: first compute the total in the unit you were given, then convert to the unit the question asks for. Here that means seconds first (300 × 2 = 600), minutes second (600 ÷ 60 = 10).

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