Speed, Time and Distance
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Solved Examples
Study MaterialSolved Examples – Speed, Time and Distance
Solved examples help students understand the practical application of Speed, Time and Distance concepts in competitive examinations. These examples are designed from basic to advanced level and cover important problems frequently asked in SSC, Banking, Railway, CDS, NDA, CAT, UPSC, Defence, and placement aptitude tests.
Topics Covered in Solved Examples
- Basic Speed Formula Problems
- Average Speed Questions
- Relative Speed Problems
- Train Problems
- Boats and Streams
- Race Problems
- Circular Track Questions
- Unit Conversion Problems
- Percentage Change in Speed
- Advanced Speed Applications
Example 1: Basic Speed Formula
Question: A car travels 240 km in 4 hours. Find its speed.
Solution:
Speed:
= Distance / Time
= 240/4
= 60 km/h
Therefore:
Speed = 60 km/h
Example 2: Finding Distance
Question: A train runs at 72 km/h for 5 hours. Find the distance travelled.
Solution:
Distance:
= Speed × Time
= 72 × 5
= 360 km
Therefore:
Distance travelled = 360 km
Example 3: Finding Time
Question: A bus travels 300 km at 50 km/h. Find the time taken.
Solution:
Time:
= Distance / Speed
= 300/50
= 6 hours
Therefore:
Time taken = 6 hours
Example 4: km/h to m/s Conversion
Question: Convert 90 km/h into m/s.
Solution:
Conversion formula:
= 90 × 5/18
= 25 m/s
Therefore:
90 km/h = 25 m/s
Example 5: m/s to km/h Conversion
Question: Convert 20 m/s into km/h.
Solution:
Conversion formula:
= 20 × 18/5
= 72 km/h
Therefore:
20 m/s = 72 km/h
Example 6: Average Speed for Equal Distances
Question: A person travels equal distances at 60 km/h and 40 km/h. Find the average speed.
Solution:
Average speed:
= 2xy / (x + y)
= (2 × 60 × 40)/(60 + 40)
= 4800/100
= 48 km/h
Therefore:
Average speed = 48 km/h
Example 7: Relative Speed (Opposite Direction)
Question: Two trains move in opposite directions at 60 km/h and 40 km/h. Find their relative speed.
Solution:
Relative speed:
= 60 + 40
= 100 km/h
Therefore:
Relative speed = 100 km/h
Example 8: Relative Speed (Same Direction)
Question: Two cars move in the same direction at 80 km/h and 50 km/h. Find their relative speed.
Solution:
Relative speed:
= 80 − 50
= 30 km/h
Therefore:
Relative speed = 30 km/h
Example 9: Train Crossing a Pole
Question: A train 180 meters long crosses a pole in 12 seconds. Find the speed of the train.
Solution:
Speed:
= Distance / Time
= 180/12
= 15 m/s
Convert into km/h:
= 15 × 18/5
= 54 km/h
Therefore:
Speed of train = 54 km/h
Example 10: Train Crossing a Platform
Question: A train 200 meters long crosses a platform 300 meters long in 25 seconds. Find the speed of the train.
Solution:
Total distance:
= 200 + 300
= 500 meters
Speed:
= 500/25
= 20 m/s
Convert into km/h:
= 20 × 18/5
= 72 km/h
Therefore:
Speed of train = 72 km/h
Example 11: Two Trains Crossing
Question: Two trains 120 m and 180 m long move in opposite directions at 54 km/h and 36 km/h. Find the time taken to cross each other.
Solution:
Total length:
= 120 + 180
= 300 m
Relative speed:
= 54 + 36
= 90 km/h
Convert into m/s:
= 90 × 5/18
= 25 m/s
Time:
= 300/25
= 12 seconds
Therefore:
Required time = 12 seconds
Example 12: Boats and Streams
Question: Speed of a boat in still water is 12 km/h and speed of stream is 3 km/h. Find downstream speed.
Solution:
Downstream speed:
= Boat speed + Stream speed
= 12 + 3
= 15 km/h
Therefore:
Downstream speed = 15 km/h
Example 13: Upstream Speed
Question: A boat moves at 20 km/h in still water and stream speed is 4 km/h. Find upstream speed.
Solution:
Upstream speed:
= Boat speed − Stream speed
= 20 − 4
= 16 km/h
Therefore:
Upstream speed = 16 km/h
Example 14: Finding Boat Speed
Question: Downstream speed is 18 km/h and upstream speed is 10 km/h. Find speed of boat in still water.
Solution:
Boat speed:
= (18 + 10)/2
= 14 km/h
Therefore:
Boat speed = 14 km/h
Example 15: Finding Stream Speed
Question: Downstream speed is 22 km/h and upstream speed is 14 km/h. Find stream speed.
Solution:
Stream speed:
= (22 − 14)/2
= 4 km/h
Therefore:
Stream speed = 4 km/h
Example 16: Circular Track Problem
Question: Two runners move on a circular track of 400 meters at speeds of 10 m/s and 15 m/s in the same direction. Find the time taken by the faster runner to catch the slower runner.
Solution:
Relative speed:
= 15 − 10
= 5 m/s
Time:
= 400/5
= 80 seconds
Therefore:
Required time = 80 seconds
Example 17: Percentage Change in Speed
Question: A man increases his speed by 25%. Find percentage reduction in time.
Solution:
Reduction in time:
= [25/(100 + 25)] × 100
= 25/125 × 100
= 20%
Therefore:
Reduction in time = 20%
Example 18: Advanced Average Speed Problem
Question: A person travels first 120 km at 60 km/h and next 180 km at 90 km/h. Find average speed.
Solution:
Total distance:
= 120 + 180
= 300 km
Time for first part:
= 120/60
= 2 hours
Time for second part:
= 180/90
= 2 hours
Total time:
= 4 hours
Average speed:
= 300/4
= 75 km/h
Therefore:
Average speed = 75 km/h
Important Exam Tips
- Always convert units properly before calculations.
- Use relative speed carefully.
- Memorize train and boat formulas.
- Use harmonic mean for equal distance problems.
- Simplify ratios before solving.
- Practice train crossing problems regularly.
- Verify calculations properly.
Practicing solved examples regularly improves conceptual clarity, logical thinking, and calculation speed in solving Speed, Time and Distance questions in competitive examinations.