Question 3
The duration, in minutes, of all activities in a project are shown.
| Activity | P | Q | R | S | T | U | V |
|---|---|---|---|---|---|---|---|
| Duration | 38 | 42 | 32 | 34 | 16 | 14 | 26 |
The critical path for the project is PRSV.
What is the earliest completion time for the project if it starts at 11:00 am?
Not quite. One way to get this is to read 130 minutes as 1 hour 30 minutes, as if the digits split into hours and minutes. An hour is 60 minutes, so 130 minutes is 2 h 10 min. In 2023, 5.1% of Queensland students chose (A).
That’s it. Step through the hints below to see why. In 2023, 79.9% of Queensland students chose (B).
Not quite. One way to get this is to read the total of 130 as the clock time 1:30. The 130 is a number of minutes, and it has to be added to the 11:00 am start. In 2023, 6.1% of Queensland students chose (C).
Not quite. 2 h 10 min is how long the project takes. One way to get 2:10 pm is to write that duration down as the finish time without adding it to the 11:00 am start. In 2023, 8.3% of Queensland students chose (D).
Switch activities on to lay them end to end from 11:00 am. The orange line is when the last one finishes. Grey blocks are off the critical path.
The critical path is the longest path through the project, so its length is the minimum time to finish everything. The other activities fit alongside it.
Add only the four activities on PRSV:
$$38+32+34+26=130\text{ min}$$
Adding all seven gives a longer time that isn’t one of the options. Press All seven on the left to see it.
Convert to hours and minutes before you touch the clock. An hour is 60 minutes, so take out as many 60s as fit:
$$130=60+60+10=2\text{ h }10\text{ min}$$
The trap is reading 130 like a clock, as 1 h 30 min or 1:30. Minutes don’t work in hundreds.
The question asks for a completion time, so add the duration to the start:
$$\text{11:00 am}+2\text{ h}=\text{1:00 pm},\qquad \text{1:00 pm}+10\text{ min}=\text{1:10 pm}$$
Check it on the timeline: the orange line sits just past the 1:00 pm tick.
$$\begin{aligned}\text{PRSV}&=38+32+34+26=130\text{ min}\\&=2\text{ h }10\text{ min}\\\text{11:00 am}+2\text{ h }10\text{ min}&=\text{1:10 pm}\end{aligned}$$
The project can finish no earlier than 1:10 pm.
Only mark this done when you could do it without help. Reading the solution does not count.
Question wording is from the 2023 QCAA General Mathematics external assessment, © State of Queensland (QCAA) 2023, licensed under CC BY 4.0, and has been adapted. Tangent Tuition is not affiliated with the QCAA.
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