PCR Van Timeline and a Faulty Witness Inference
At the Model Town police post, the day's PCR log has to be closed before the night shift hands over. The van left the post at 21:10 with a two-constable crew and returned at 21:40. The log records a route of 12 km with a single six-minute halt at the bus stand, which lies 5 km from the post; the crew claims an average speed of 30 km/h. The market chowk lies 7 km along the same route.
Two statements are on file. Witness A says the van was standing at the market chowk at 21:35. Witness B says the van was at the bus stand at about 21:20 and had already crossed the market chowk before 21:25. The shop CCTV at the chowk is known to run eight minutes fast.
Separately, a constable offers this argument for the diary: 'All constables on night duty carry a torch. Some people who carry a torch also carry a wireless set. Therefore some constables on night duty carry a wireless set.'
1. Reconstruct the van's timeline minute by minute. Can Witness A's sighting at 21:35 be accepted, or should A be treated as making a false statement?
Read the worked answer
Step 1 - Check the log for internal consistency. Total time on duty = 21:10 to 21:40 = 30 minutes. Travel time at 30 km/h for 12 km = 12 ÷ 30 × 60 = 24 minutes. Add the 6-minute halt = 30 minutes. The log is arithmetically consistent, so the claimed speed and halt are believable.
Step 2 - Build the timeline.
- 21:10 - leaves post.
- Bus stand, 5 km: 5 ÷ 30 × 60 = 10 min → arrives 21:20.
- Halt 6 min → leaves 21:26.
- Market chowk, 2 km further: 2 ÷ 30 × 60 = 4 min → arrives 21:30.
- Remaining 5 km back to post: 10 min → 21:40. Matches the return time.
Step 3 - Test Witness A. A says 21:35, the reconstruction says 21:30 - a gap of 5 minutes. That gap is not decisive: a crowded chowk, a slower stretch, or a longer halt easily absorbs it.
Step 4 - Apply the known clock error. The CCTV runs 8 minutes fast, so a CCTV stamp of 21:38 corresponds to a true time of 21:30 - an exact match with the reconstruction. A's statement therefore fits the physical evidence once the clock skew is corrected.
Conclusion: A's sighting is corroborated, not contradicted. Do not treat A as hostile; instead record the clock-correction reasoning in the diary, and settle the halt duration from the PCR log and the van's GPS track if available.
2. Test Witness B's statement against your reconstruction. What does the result mean for the investigation, and what should the constable do next?
Read the worked answer
The statement is self-contradictory on the route itself. B places the van at the bus stand at about 21:20 (which agrees with the reconstruction) and also says it had crossed the market chowk before 21:25. But the chowk lies after the bus stand on the route, and the six-minute halt at the bus stand does not end until 21:26. The van cannot be at the chowk, 2 km beyond, before it has even left the bus stand.
Earliest possible arrival at the chowk = 21:26 + 4 min = 21:30. Any claim of 'before 21:25' is impossible unless the halt was skipped, the route order is different, or the witness is guessing.
What this means:
- B is either confusing the order of landmarks (common in a short, dark stretch) or reconstructing from hearsay rather than observation.
- B is not automatically a false witness - a wrong sequence is different from a deliberate lie.
Next steps for the constable:
- Re-record B's statement, asking B to name the landmarks in the order seen and to fix the position of the bus stand relative to the chowk.
- Show B the route sketch and ask for the direction of travel.
- Cross-check with any other independent witness at the bus stand.
- Only if B persists after the route is demonstrated should the statement be treated as doubtful, and even then the diary should record the contradiction, not a conclusion of lying.
A reconstruction that is physically impossible is the strongest tool available; use it to re-interview, not to accuse.
3. Is the constable's argument ('All night-duty constables carry a torch; some torch-carriers carry a wireless set; therefore some night-duty constables carry a wireless set') valid? Rewrite the reasoning correctly.
Read the worked answer
It is invalid - an undistributed-middle fallacy. Both premises talk about 'people who carry a torch', but they need not be talking about the same torch-carriers. The 'some torch-carriers' with wireless sets may all be day-shift staff, in which case the premises are true and the conclusion false.
Counter-example:
- Night-duty constables = {P, Q}; both carry torches. Premise 1 true.
- Torch-carriers with wireless sets = {R, S}, both day staff. Premise 2 true.
- Conclusion 'some night-duty constables carry a wireless set' is false.
Since a situation exists where the premises hold and the conclusion fails, the argument is not valid.
What would make it valid:
- 'All who carry a torch also carry a wireless set' (then every night-duty constable carries one), or
- 'No day-shift constable carries a torch' (then the torch-carriers with wireless sets must be night staff).
Correct conclusion from the given premises: none about night-duty constables. The argument proves nothing.
Why it matters in a police station: a diary entry that presents an invalid inference as a deduction can be demolished in cross-examination. If the point is worth recording at all, write it as a hypothesis to be checked - 'verify whether night-duty staff have been issued wireless sets' - and then verify it against the register, not by argument.