Final answer:
To calculate the project length, one must analyze the dependencies and complete a Critical Path Method. The longest path for the given tasks (A-C-D-E-F-G) totals 151 hours, indicating the project length is 151 hours.
Step-by-step explanation:
The question asks how long the project will take given the time estimates for each task and their predecessors. To determine the project length, one needs to consider the dependencies of each task and construct a schedule that accommodates them, commonly known as a Critical Path Method (CPM) analysis.
Here is the breakdown of the tasks:
- Task A takes 40 hours and has no predecessor.
- Task B takes 20 hours and has no predecessor.
- Task C takes 25 hours and can only start after Task A is completed.
- Task D takes 19 hours and can start after Task A and Task B are completed.
- Task E takes 25 hours and can start after Task C and D are completed.
- Task F takes 24 hours and can start after Task E is completed.
- Task G takes 18 hours and can start after Task F is completed.
The sum of all these tasks does not represent the total project length, as some tasks can be done in parallel. The project's length is equal to the duration of the longest path through these tasks. This path is A-C-D-E-F-G, which totals 151 hours: 40 (A) + 25 (C) + 19 (D) + 25 (E) + 24 (F) + 18 (G).
Therefore, the project length is 151 hours.