Night-beat loop: fuel, time and where to spend the extra twenty minutes
You are handed the night-beat plan for the 22:00–06:00 shift. The station has one jeep with 8 litres in the tank and a normal mileage of 12 km per litre. The outer loop runs HQ → Chowk A (6 km) → Bazaar B (9 km) → Bus Stand C (7 km) → HQ (10 km). Standing orders require two full rounds per shift, with a 10-minute foot halt at each of A, B and C on every round; the jeep averages 24 km/h on the route, and halt time is counted separately. One litre must always be kept in reserve. Thirty-day night-crime data show 12 incidents in A, 5 in B and 3 in C; A is a closed-shutter commercial market, B a residential mohalla, and C an interstate bus stand with a 24-hour waiting hall. At the end of the first round the driver reports a clogged filter: mileage has dropped to 9 km per litre and the tank reads 5.2 litres.
1. Using the normal mileage, compute the total distance, fuel requirement and finishing time of the planned shift.
Read the worked answer
Loop length = 6 + 9 + 7 + 10 = 32 km; two rounds = 64 km.
Driving time = 64 ÷ 24 = 2.667 h = 2 h 40 min.
Halts = 3 points × 2 rounds × 10 min = 60 min.
Total = 3 h 40 min, so a 22:00 start returns at 01:40, leaving 4 h 20 min of shift unused - the plan is not time-constrained.
Fuel = 64 ÷ 12 = 5.33 litres. Usable fuel before reserve = 8 − 1 = 7 litres. The plan is feasible with about 1.67 litres spare, which matters because idling at halts and low-gear lane work will always consume more than the rated figure. The correct answer therefore states 64 km, 5.33 litres, and 01:40, and notes that the constraint on this shift is fuel, not time.
2. Given the mileage drop to 9 km/l and 5.2 litres in the tank at the end of round one, is the second round feasible? Show the arithmetic and state your decision.
Read the worked answer
Second round = 32 km at 9 km/l = 3.56 litres.
Fuel available = 5.2 litres; after keeping the 1-litre reserve, usable = 4.2 litres.
Margin = 4.2 − 3.56 = 0.64 litres, roughly 5.8 km at the degraded mileage. So the round is feasible but thin, and the margin disappears if mileage falls further (at 7 km/l the round needs 4.57 litres, more than the usable 4.2).
Decision: complete the second round, but (i) send a constable to bring a filled jerrycan from the station before the jeep leaves HQ on round two - this costs no distance, unlike a 3-km detour to a pump, which would burn 0.33 litre and eat half the margin; (ii) switch off the engine at every halt, since idling is what breaks mileage figures; (iii) radio the control room the degraded mileage so the shift is not planned on paper figures again.
3. The inspector allows you 20 extra minutes beyond the standing halts. Using the data and the character of the three points, where do you spend it, and what are the limits of the raw incident counts?
Read the worked answer
Raw counts (A 12, B 5, C 3) cannot be read as risk without exposure. A is a commercial market with roughly 40 shutters but almost no residents at night - high opportunity, low guardianship, but also a place where incidents get reported by shopkeepers in the morning. C is a 24-hour bus stand with a continuous flow of strangers and no settled population to watch it: exposure per hour is highest there, and the people who suffer are travellers who leave before lodging a complaint, so its 3 incidents are the most under-reported number on the sheet. B is residential, where residents report readily and the chance of an incident being seen is higher.
So: keep all three halts, and place the extra 20 minutes at C during the 02:00–04:00 arrival window, foot-patrolling the waiting hall and the ticket queue. At A, the jeep stop covers only the main road - use part of the A halt to walk the lane behind the market, which the loop never touches. Record in the diary where the extra time was spent and why, so the next shift can build on it.