Time‑Speed‑Distance – Study Notes
(Quantitative Aptitude – West Bengal Forest Guard Program)
1. Simple Explanation
| Term | What it means | Symbol | Units |
|---|---|---|---|
| Distance (S) | The total ground covered | (S) | km, m, etc. |
| Speed (V) | The rate of motion | (V) | km/h, m/s |
| Time (T) | The duration taken | (T) | hrs, min, s |
Fundamental Relation
[ \boxed{S = V \times T} ]
Speed = Distance ÷ Time
Time = Distance ÷ Speed
Distance = Speed × Time
2. Key Points
| Point | Details |
|---|---|
| Units must match | If speed is in km/h, time must be in hours; if you use minutes, convert to hours first. |
| Speed can be constant or average | In most exam problems speed is average unless stated otherwise. |
| Direction matters only when sign is used | For simple distance‑speed‑time problems, direction is ignored. |
| Conversion | 1 hour = 60 minutes; 1 km = 1000 m. |
| Common mistake | Forgetting to convert minutes to hours before multiplication. |
| Speed change | If a vehicle changes speed, treat each segment separately and add distances or times. |
| Units of speed | Use km/h for road travel, m/s for walking/running, etc. |
3. Worked Example
Problem (typical for FG exams)
A forest guard drives a jeep from Station A to Station B, covering 120 km. The first 60 km are travelled at 60 km/h, the remaining 60 km at 40 km/h. What is the total time taken for the journey?
Step‑by‑Step Solution
| Segment | Distance (km) | Speed (km/h) | Time (hrs) | Calculation |
|---|---|---|---|---|
| 1 | 60 | 60 | (60 ÷ 60 = 1) | 1 hr |
| 2 | 60 | 40 | (60 ÷ 40 = 1.5) | 1.5 hrs |
| Total | 120 | – | (1 + 1.5 = 2.5) | 2.5 hrs |
Answer: The jeep takes 2.5 hours (i.e., 2 hrs 30 min) to travel from A to B.
Quick Checklist
- Convert speeds to same unit (km/h).
- Compute time for each segment separately.
- Add times for total.
- Convert to hrs/min if required.
4. Quick Revision Summary
-
Formulae
- (S = V \times T)
- (V = \dfrac{S}{T})
- (T = \dfrac{S}{V})
-
Unit conversion
- Minutes → Hours: divide by 60.
- km → m: multiply by 1000 (use only if needed).
-
Solve in order
- Identify what is given (S, V, T).
- Check units, convert if necessary.
- Choose the right formula.
- Perform calculation carefully.
- Verify units of answer.
-
Common pitfalls
- Mixing minutes with hours.
- Forgetting to add times when speed changes.
- Misreading “average speed” vs “instantaneous speed”.
-
Practice Tips
- Work through at least 5 problems with varying conditions (constant speed, changing speed, round‑trip).
- Time yourself to improve speed under exam conditions.
- Double‑check that the final answer’s units match the question’s requirement.
Good luck, Forest Guard aspirants!
Master these basics, and you’ll crack the Time‑Speed‑Distance section with confidence.