Time & Distance
Overview
Time & Distance is a fundamental quantitative topic that appears consistently in Maharashtra Police Bharti exams. This chapter tests your ability to apply the basic relationship between speed, time, and distance to various practical scenarios—moving vehicles, trains crossing platforms, and boats navigating rivers.
The questions typically range from straightforward speed calculations to slightly complex problems involving relative speed (trains) and effective speed (boats in streams). Mastering this topic requires memorizing key formulas and developing the skill to quickly identify which formula applies to a given situation. Since police work involves understanding vehicle speeds, patrol timings, and distance coverage, this topic has practical relevance beyond the exam.
Most problems can be solved within 30-60 seconds if you know the formulas and unit conversions by heart.
Key Concepts
- Basic Relationship: Speed = Distance ÷ Time. This formula rearranges to Distance = Speed × Time and Time = Distance ÷ Speed.
- Unit Conversion: Converting between km/hr and m/s is essential—multiply km/hr by 5/18 to get m/s, and multiply m/s by 18/5 to get km/hr.
- Relative Speed (Same Direction): When two objects move in the same direction, relative speed = difference of their speeds.
- Relative Speed (Opposite Direction): When two objects move toward each other, relative speed = sum of their speeds.
- Train Problems: The distance covered by a train includes its own length. When crossing a platform, total distance = length of train + length of platform.
- Boats & Streams: A boat's effective speed changes based on water current—downstream (with current) speed increases, upstream (against current) speed decreases.
- Average Speed: When covering the same distance at two different speeds, average speed = 2ab/(a+b), not the simple arithmetic mean.
Formulas / Key Facts
| Situation | Formula |
|---|---|
| Basic | Speed = Distance/Time |
| km/hr to m/s | Multiply by 5/18 |
| m/s to km/hr | Multiply by 18/5 |
| Train crossing a pole/person | Time = Length of train ÷ Speed |
| Train crossing a platform/bridge | Time = (Length of train + Length of platform) ÷ Speed |
| Two trains crossing each other (opposite direction) | Time = (L₁ + L₂) ÷ (S₁ + S₂) |
| Two trains crossing each other (same direction) | Time = (L₁ + L₂) ÷ (S₁ - S₂) |
| Downstream speed | Boat speed + Stream speed |
| Upstream speed | Boat speed - Stream speed |
| Speed of boat in still water | (Downstream + Upstream) ÷ 2 |
| Speed of stream | (Downstream - Upstream) ÷ 2 |
| Average speed (same distance, two speeds) | 2ab/(a+b) |
Worked Examples
Example 1: Basic Speed Calculation
Problem: A car travels 240 km in 4 hours. Find its speed in m/s.
Solution:
- Speed = Distance ÷ Time = 240 ÷ 4 = 60 km/hr
- Convert to m/s = 60 × 5/18 = 300/18 = 50/3 = 16.67 m/s
Answer: 16.67 m/s (or 50/3 m/s)
Example 2: Train Crossing a Platform
Problem: A train 150 m long crosses a 250 m platform in 20 seconds. Find the speed of the train in km/hr.
Solution:
- Total distance = Train length + Platform length = 150 + 250 = 400 m
- Speed = Distance ÷ Time = 400 ÷ 20 = 20 m/s
- Convert to km/hr = 20 × 18/5 = 72 km/hr
Answer: 72 km/hr
Example 3: Boats and Streams
Problem: A boat travels 36 km downstream in 3 hours and returns upstream in 6 hours. Find the speed of the boat in still water and the speed of the stream.
Solution:
- Downstream speed = 36 ÷ 3 = 12 km/hr
- Upstream speed = 36 ÷ 6 = 6 km/hr
- Speed of boat in still water = (12 + 6) ÷ 2 = 9 km/hr
- Speed of stream = (12 - 6) ÷ 2 = 3 km/hr
Answer: Boat speed = 9 km/hr, Stream speed = 3 km/hr
Example 4: Two Trains Crossing Each Other
Problem: Two trains of lengths 120 m and 80 m are running in opposite directions at 50 km/hr and 40 km/hr. In how many seconds will they cross each other?
Solution:
- Total distance = 120 + 80 = 200 m
- Relative speed = 50 + 40 = 90 km/hr (opposite direction, so add)
- Convert to m/s = 90 × 5/18 = 25 m/s
- Time = 200 ÷ 25 = 8 seconds
Answer: 8 seconds
Common Mistakes
- Forgetting train's own length → When a train crosses a stationary object (pole/person), students forget that the train must cover its entire length. Always include train length in distance.
- Adding speeds for same direction → Students add speeds when objects move in the same direction. Correct fix: Subtract speeds when moving same direction, add when moving opposite.
- Wrong unit conversion → Confusing 5/18 and 18/5. Remember: km/hr is a bigger number than m/s for the same speed, so multiply by the fraction that makes it smaller (5/18) when converting km/hr to m/s.
- Using arithmetic mean for average speed → When traveling equal distances at different speeds, average speed ≠ (a+b)/2. Correct formula: 2ab/(a+b).
- Confusing downstream and upstream → Downstream means going WITH the current (faster), upstream means going AGAINST the current (slower). Think: "Down" = water helps you = add speeds.
Quick Reference
- Speed = Distance/Time — the master formula for all problems.
- km/hr to m/s: × 5/18 | m/s to km/hr: × 18/5
- Opposite direction → ADD speeds | Same direction → SUBTRACT speeds
- Train crossing platform = (Train length + Platform length) ÷ Speed
- Boat still water speed = (Downstream + Upstream) ÷ 2
- Stream speed = (Downstream - Upstream) ÷ 2
- Average speed for equal distances = 2ab/(a+b), not (a+b)/2