This question's explanation and your answers so far.
ある機械の組立て作業のメンバになった P さんは，リーダの指導の下，作業工程を確認するためにアローダイアグラムを作成した。作成したアローダイアグラムは，効率よく作業を進行させるために，メンバ間で共有することにした。図 1 にアローダイアグラムを示す。 各工程は 1 人で行うものとして計画し，メンバの誰が担当しても予定日数で作業を終了するものとする。 図1の工程1と工程2はPさんが担当することになった。工程1が予定日数どおりに完了した後，工程2の開始前に会社を休むことにした。工程2が予定日数どおりに完了すると仮定して，プロジェクトの進行に影響が出ないようにするためには，Pさんは工程2の開始前に最大何日間休むことができるか。ここで，休日の日数は考えないものとする。
※ Our check while writing this explanation could not fully confirm the published answer; scoring follows IPA's official key.
Resting only 1 day indeed does not affect the overall progress, but process 2 still has float remaining, so this is not the maximum. The question asks for the maximum number of days that can be taken off, and 1 day — which does not use up all the float — falls short and is therefore wrong.
正解 In an arrow diagram (PERT chart), a process that is not on the critical path (the longest path) has an amount of float (slack days) during which its start can be delayed without affecting the later processes or the project’s overall completion date. What this question asks — the maximum number of days P can rest before process 2 starts — is exactly equal to this float that process 2 has. In the schedule of Figure 1, process 2 has 2 days of float, so even if the start of process 2 is delayed by 2 days after process 1 finishes on schedule, the project’s overall completion date will not change as long as process 2 is completed in its planned number of days. Therefore P can rest at most 2 days, and the correct answer is イ. Delaying 3 or more days exceeds the float and pushes back the overall completion.
If P rests 3 days, the start of process 2 is delayed by 1 day beyond the float (2 days). Even if process 2 finishes in its planned number of days, the project’s overall completion is delayed by 1 day, affecting the progress, so it is wrong.
If P rests 4 days, the start of process 2 is delayed far beyond the float, causing the project’s completion to be delayed. This clearly affects the overall schedule, so it is wrong.