63. Trucks (10 m long) and card (5 m long) go on a single lane bridge. There must be a gap of at least 20
m after each truck and a gap of at least 15 m after each car. Trucks and cars travel at a speed of 36
km/h. If cars and trucks go alternately, what is the maximum number of vehicles that can use the bridge
in one hour?
(a) 1440 (b) 1200
(c) 720 (d) 600

Problem Setup

Trucks and cars alternate on a single-lane bridge with strict safety gaps, limiting throughput at 36 km/h.

Maximum number of vehicles per hour = 1440.

• Truck length: 10 m + 20 m gap = 30 m effective length
• Car length: 5 m + 15 m gap = 20 m effective length
• Alternating pairs (truck + car) create a 50 m cycle

Speed Conversion

36 km/h × (1000 / 3600) = 10 m/s

Cycle Calculation

Time to clear one alternating pair:

Time = 50 m ÷ 10 m/s = 5 seconds

Hourly Capacity

• Seconds per hour = 3600
• Cycles per hour = 3600 ÷ 5 = 720
• Vehicles per cycle = 2 (1 truck + 1 car)

Total vehicles per hour:

720 × 2 = 1440

Option Analysis

• (a) 1440 — Correct, derived from cycle time × vehicles per cycle
• (b) 1200 — Incorrect; likely from faulty conversion
• (c) 720 — Considers cycles but forgets two vehicles per cycle
• (d) 600 — No mathematical basis

Key Parameters Summary

• Truck effective length: 30 m
• Car effective length: 20 m
• Alternate cycle = 50 m
• Speed = 10 m/s
• Vehicles/hour = 1440

Why Alternating Maximizes Flow

The alternating pattern ensures:

• No gap overlap
• Consistent spacing
• 50 m cycle regardless of whether the truck or car leads

Common Errors

• Using cycle output instead of vehicle output: 720
• Mistaken speed conversions
• Ignoring order (car-first still yields 50 m)

Keywords

maximum vehicles bridge one hour, trucks cars alternately, 36 km/h bridge gap problem, GATE aptitude traffic flow