What changes the fastest path?
Draw two checks and the point where their paths join.
The question
Two workers prepare to move a crate at a fictional museum. Both checks can start at the same time. Each worker has a scanner.
| Minutes | |
|---|---|
| Check crate label | 4 |
| Check rack label | 6 |
| Move crate | 3 |
Both checks must finish before the move. There is no waiting, setup or interruption.
- Check A
- Crate label → Ready
- Check B
- Rack label → Ready
- Join
- Both ready → Move crate
“Which path is quicker, and what would you redraw if the resources change?”
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A strong answer, step by step
Open each step in turn. This is one strong answer, not the only one.
Step 1: Which paths can run together?
What would you do here? Open the move you’d make.
Start moving once either check finishes
Tempting, but it misses something. The move requires both results.
Draw parallel checks and an explicit join
The strong move. The join shows that both checks must finish.
Draw a dependency from crate check to rack check
Tempting, but it misses something. The opening packet gives no reason for one check to wait.
See how a strong candidate says it
“I’ll put the crate and rack checks on separate paths. They join at Both ready before the move.”
Why it works: Each worker has a scanner and neither check needs the other to finish.
Step 2: Which sketch is quicker?
What would you do here? Open the move you’d make.
Compare nine minutes in parallel with 13 in sequence
The strong move. The diagram makes the overlap and join visible.
Add four, six and three for both diagrams
Tempting, but it misses something. That ignores the overlap in the two-scanner sketch.
Use four plus three for the parallel diagram
Tempting, but it misses something. The six-minute check would still be running.
See how a strong candidate says it
“With two scanners the longer check takes six minutes. Then the move takes three, for nine total. Sequential checks take ten plus three, for 13.”
Why it works: Parallel checks overlap. The move still takes three minutes after both checks.
Step 3: What changes with one scanner?
Both workers must share one scanner. Each check uses it continuously and the durations stay the same.
What would you do here? Open the move you’d make.
Keep both checks starting together
Tempting, but it misses something. The revised setup has only one scanner.
Remove the rack check to keep nine minutes
Tempting, but it misses something. The move still requires both checks.
Draw the shared scanner as a reason to put the checks in sequence
The strong move. This changes the timing while preserving the requirement for both results.
See how a strong candidate says it
“I’ll show the checks in sequence and put the move after both. With one scanner, four plus six plus three gives 13 minutes.”
Why it works: Each check needs the scanner throughout, so their durations cannot overlap.
Step 4: What changed the timing?
What would you do here? Open the move you’d make.
Say that moving the crate now takes seven minutes
Tempting, but it misses something. The move still takes three. The checks take longer together.
Name the shared resource and trace the ten-minute join
The strong move. The interviewer can see what made the plan four minutes longer.
Say the order decides whether 13 minutes is possible
Tempting, but it misses something. With no setup or idle time either order takes ten minutes before the move.
See how a strong candidate says it
“The scanner is now shared. Both checks finish after ten minutes, and the move ends at 13. Starting the move at six would leave a check unfinished.”
Why it works: The explanation points to the changed resource and the required join.
The answer, in short
- Decision
- Use a sequential pair of checks with one scanner.
- Because
- One scanner cannot run the two checks together. The total increases from nine to 13 minutes.
- What would change it
- With two scanners, the independent checks can overlap again.
Common traps
- Starting the move when one check finishes
- Keeping parallel paths after a shared resource appears
Check your answer
- Where do the checks join?
- How long is the parallel path?
- What prevents overlap after the change?
- When can the move start?
Last reviewed Nov 11, 2026