Question 1
The float time, in minutes, for the non-critical activity of this project network is
Not quite. 10 minutes is how long Watch the news takes, its duration. Float is the spare time around an activity: how long it can be delayed without making the whole project late. In 2022, 33.9% of Queensland students chose (A).
That’s it. Step through the hints below to see why. In 2022, 36.7% of Queensland students chose (B).
Not quite. One way to get 23 is $33-10$, the latest time Watch the news could start. That is measured from minute 0, but the activity can’t start before minute 3, so it can only be pushed back by $23-3$ minutes. In 2022, 13.4% of Queensland students chose (C).
Not quite. One way to get 30 is $33-3$, the whole window between the earliest start and the latest finish. Watch the news uses 10 minutes of that window, so only 20 are spare. In 2022, 14.8% of Queensland students chose (D).
The same project on a timeline. Drag the slider to start Watch the news later and see how far you can push it before dinner runs late.
Black bars, left to right: Collect ingredients 3, Turn on oven 5, Prepare ingredients 8, Cook food 17, Eat food 5. Blue dashed lines: minute 3, when Watch the news can start, and minute 33, when it must be finished so Eat food can start on time.
Every node on the bottom row has the same number on both sides, and each activity along the bottom exactly fills the gap between its two nodes (3, 5, 8, 17 and 5 minutes), so every activity along the bottom is critical. The one activity off that path is Watch the news, the curved arrow.
Read its two ends. It leaves the 3 | 3 node, so the earliest it can start is minute 3. It arrives at the 33 | 33 node, so it must be finished by minute 33, or Eat food starts late.
That gives Watch the news a window of 30 minutes, and it only needs 10 of them. Whatever is left over is the float.
$$\begin{aligned}\text{float}&=\text{LST at the end}-\text{EST at the start}-\text{duration}\\&=33-3-10\\&=20\text{ minutes}\end{aligned}$$
On the timeline, slide the start from 3 to 23 and the activity still finishes by 33. That is 20 minutes of delay it can absorb.
Check it another way. While Watch the news runs, the critical path is busy with Turn on oven, Prepare ingredients and Cook food:
$$5+8+17=30\text{ minutes, and }30-10=20$$
The other three options are each a real number from the network, just not the float. Press “Where do the four options come from?” on the left to see all four lengths side by side.
The non-critical activity is Watch the news. It starts at the 3 | 3 node and ends at the 33 | 33 node.
$$\begin{aligned}\text{float}&=\text{LST at the end}-\text{EST at the start}-\text{duration}\\&=33-3-10\\&=20\text{ minutes}\end{aligned}$$
Watch the news can be delayed by up to 20 minutes without making the project late.
Only mark this done when you could do it without help. Reading the solution does not count.
Question wording is from the 2022 QCAA General Mathematics external assessment, © State of Queensland (QCAA) 2022, licensed under CC BY 4.0, and has been adapted. Tangent Tuition is not affiliated with the QCAA.
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