Time, Speed and Distance made clear.
Keep all units consistent and think about the distance that actually closes or gets covered. Relative speed and average speed become straightforward once the journey is drawn.
Key concepts in Time, Speed and Distance
Core relationship
Distance = speed × time. Time = distance/speed.
Unit conversion
Multiply km/h by 5/18 to get m/s; multiply m/s by 18/5 to get km/h.
Relative speed
For motion along one straight line, opposite directions add speeds; same-direction pursuit uses the difference.
Average speed
Total distance / total time. For equal distances at speeds a,b, it is 2ab/(a+b).
Trains and boats
A train passing a pole covers its own length; passing a platform covers both lengths. Downstream speed = still-water speed + stream speed.
Equal-distance journey
| Leg | Distance | Speed | Time |
|---|---|---|---|
| Outward | 60 km | 30 km/h | 2 h |
| Return | 60 km | 60 km/h | 1 h |
| Whole trip | 120 km | 40 km/h average | 3 h |
A reliable solving method
- Sketch the route and mark the distance to be covered.
- Choose one set of units before calculating.
- Use relative speed only for the relative separation being closed.
- Add all journey times, including stops when specified.
Step-by-step solved examples
Travel 150 km at 50 km/h. Find time.
- Time = distance/speed.
- 150/50 = 3 hours.
- Check: 50×3 = 150 km.
A 180 m train passes a pole at 54 km/h. Find time.
- 54×5/18 = 15 m/s.
- The train covers its own length, 180 m.
- Time = 180/15 = 12 seconds.
Travel 60 km at 30 km/h and return 60 km at 60 km/h. Average speed?
- Outbound time is 2 hours; return time is 1 hour.
- Total distance = 120 km, total time = 3 hours.
- Average = 40 km/h, not 45 km/h.
Time, Speed and Distance: practice questions
Choose one answer before opening the explanation. Write down your reasoning as well as the option; a correct guess is different from a method you can repeat.
72 km/h in m/s?
Show answer and explanation — question 1
Answer C: 20
72×5/18 = 20.
Distance at 40 km/h for 2.5 hours?
Show answer and explanation — question 2
Answer C: 100 km
40×2.5 = 100 km.
Opposite-direction speeds 30 and 50 km/h: relative speed?
Show answer and explanation — question 3
Answer D: 80
They close separation at 30+50 = 80 km/h.
Same-direction speeds 60 and 45 km/h: pursuit speed?
Show answer and explanation — question 4
Answer A: 15
60−45 = 15 km/h.
100 m train passes 200 m platform at 10 m/s. Time?
Show answer and explanation — question 5
Answer C: 30 s
Required distance = 100+200 = 300 m; time = 30 s.
Boat speed 10 km/h in still water, stream 2. Upstream speed?
Show answer and explanation — question 6
Answer A: 8
10−2 = 8 km/h.
Frequently asked questions
Why add train and platform lengths?
The rear of the train must also pass the far end of the platform.
What if upstream speed is zero?
The boat cannot make upstream progress in this constant-speed model.
Sketch the route and mark the distance to be covered. Add all journey times, including stops when specified.