Time and Distance
“Time and Distance problems are fundamental in aptitude tests, using the relationship between speed, time, and distance.”
1. Basic Concepts and Formulas
- Distance = Speed × Time
- Speed = Distance / Time
- Time = Distance / Speed
- When units differ, use: 1 km/hr = 5/18 m/sec and 1 m/sec = 18/5 km/hr
- Average Speed = Total Distance / Total Time
2. Type-Wise Questions
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Type 1: Finding Distance
Example: Speed = 60 km/hr, Time = 2 hrs. Find Distance?
Solution: Distance = 60 × 2 = 120 km
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Type 2: Finding Speed
Example: Distance = 150 km, Time = 3 hrs. Find Speed?
Solution: Speed = 150 / 3 = 50 km/hr
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Type 3: Finding Time
Example: Speed = 40 km/hr, Distance = 100 km. Find Time?
Solution: Time = 100 / 40 = 2.5 hours
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Type 4: Average Speed
Example: A covers 60 km at 30 km/hr and 60 km at 60 km/hr.
Solution: Average speed = 2 × (30×60)/(30+60) = 40 km/hr
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Type 5: Relative Speed (Same Direction)
Example: A train at 60 km/hr overtakes a man running at 6 km/hr. Relative Speed = 60 – 6 = 54 km/hr
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Type 6: Relative Speed (Opposite Direction)
Example: Two trains at 50 km/hr and 70 km/hr in opposite directions. Relative speed = 50 + 70 = 120 km/hr
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Type 7: Converting Units
Example: Convert 72 km/hr to m/s
Solution: 72 × (5/18) = 20 m/s
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Type 8: Train Passing a Pole
Example: Train length = 150 m, speed = 30 m/s. Time = 150 / 30 = 5 sec
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Type 9: Train Passing a Platform
Example: Train = 150 m, Platform = 100 m, Speed = 20 m/s. Time = (150+100)/20 = 12.5 sec
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Type 10: Boats and Streams
Example: Boat speed = 10 km/hr, Stream = 2 km/hr. Downstream = 12 km/hr, Upstream = 8 km/hr
3. Tips to Remember
- Use consistent units: convert km/hr to m/s or vice versa when needed.
- In boats & streams, Downstream = Boat + Stream, Upstream = Boat – Stream
- Relative speed is key when two bodies move toward or away from each other.
- When average speed is asked for different speeds over same distance: Use formula 2xy/(x+y)