Calculate Continuous Shared Duration

Supplied materials

• Paper and a pencil, typed notes or a browser scratch area. Color names can replace colored supplies; drawn figures and timelines can replace performance.
• Complete teaching inputs: In an original arrangement timeline, lineA runs from time 0 to 4, and lineB from time 1 to 4, with intervals treated half-open. How long do both lines overlap? Supplied candidates: (A) 2 time units (B) 3 time units (C) 4 time units (D) 5 time units.
• Independent check: In an original arrangement timeline, lineA runs from time 0 to 5, and lineB from time 2 to 5, with intervals treated half-open. How long do both lines overlap? Supplied candidates: (A) 2 time units (B) 3 time units (C) 4 time units (D) 5 time units.

Learn the idea

Inspect structure at several time scales. Calculate continuous overlap, connect a declared tonal phrase plan with its ending, distinguish tied durations from repeated onsets and preserve essential dramatic cues through synchronized visible alternatives. A continuous arrangement timeline represents elapsed time. The overlap interval begins at the later start and ends at the earlier end, so its duration is endpoint subtraction.

Reason through the supplied case: The shared time interval is [1,4). Its duration is 4−1=3. This is continuous timeline duration, not an inclusive count of beat labels; using a plus-one count would answer a different question.

Continuous duration differs from an inclusive count of beat labels. The half-open interval convention is explicitly supplied here; choose the model from the question’s requested quantity.

1. Read the complete teaching inputs and mark the feature, rule or constraint being tested.
2. Compare the model decision with one rejected candidate; state the visible evidence or calculation that distinguishes them.
3. Solve the independent check and the three changed-input practice cases before reading feedback.
4. Schedule A on time interval zero-to-six and B on two-to-six, then mark their shared interval.
5. Check your artifact against these explicit criteria: The overlap is the half-open interval two-to-six with duration four time units, without adding a beat-position count.

Check your reasoning

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Take it further

New-input analysis: In an original arrangement timeline, lineA runs from time 0 to 11, and lineB from time 2 to 11, with intervals treated half-open. How long do both lines overlap? Supplied candidates: (A) 10 time units (B) 11 time units (C) 8 time units (D) 9 time units. Expected relationship: 9 time units. The shared time interval is [2,11). Its duration is 11−2=9. This is continuous timeline duration, not an inclusive count of beat labels; using a plus-one count would answer a different question. Create your own artifact: Schedule A on time interval zero-to-six and B on two-to-six, then mark their shared interval. Completion criteria: The overlap is the half-open interval two-to-six with duration four time units, without adding a beat-position count.

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