Time – Speed – Distance (TSD)
Quantitative Aptitude – Delhi Patwari / Lekhpal Program
1. Simple Explanation
The Time‑Speed‑Distance relationship is a fundamental concept in physics and everyday life.
It expresses how long it takes to cover a distance when you know the speed, or how fast you must go to cover a distance in a given time.
[ \boxed{\text{Distance (D)} = \text{Speed (S)} \times \text{Time (T)}} ]
All three variables are inter‑related:
| Variable | Symbol | Unit | Relationship |
|---|---|---|---|
| Distance | (D) | km, m, miles, … | (D = S \times T) |
| Speed | (S) | km/h, m/s, mph, … | (S = \dfrac{D}{T}) |
| Time | (T) | hrs, mins, s, … | (T = \dfrac{D}{S}) |
Tip: Always keep the units consistent before plugging numbers into the formula.
2. Key Points to Remember
| # | Concept | What to Watch Out For |
|---|---|---|
| 1 | Unit Consistency | Convert all values to the same base unit (e.g., hours for time, km for distance) before calculation. |
| 2 | Speed vs. Pace | Speed = distance/time. Pace is the inverse: time per unit distance (useful for walking/running). |
| 3 | Average Speed | For multiple legs of a trip at different speeds, use total distance ÷ total time. |
| 4 | Speed vs. Velocity | In these problems, direction is usually ignored; we talk only about magnitude. |
| 5 | Common Ratios | 1 km = 1000 m, 1 hr = 60 min, 1 min = 60 s. |
| 6 | Converting Between Units | 1 km/h = 1000 m / 3600 s ≈ 0.2778 m/s. |
| 7 | Back‑Calculations | If you know any two variables, simply divide/multiply to find the third. |
| 8 | Time‑Speed‑Distance in Real Life | Travel distance, walking pace, cycling, train schedules, etc. |
3. Worked Example
Problem
A patwari has to reach the village 72 km away.
He can walk at 6 km/h or cycle at 12 km/h.
How much time will he save by cycling instead of walking?
Step‑by‑Step Solution
| Scenario | Speed (S) | Distance (D) | Time (T) |
|---|---|---|---|
| Walking | 6 km/h | 72 km | (T_w = \dfrac{72}{6} = 12) h |
| Cycling | 12 km/h | 72 km | (T_c = \dfrac{72}{12} = 6) h |
Time Saved
[ \text{Time Saved} = T_w - T_c = 12\text{ h} - 6\text{ h} = 6\text{ h} ]
Answer: The patwari will save 6 hours by cycling.
4. Quick Revision Summary
| Concept | Formula | Quick Tip |
|---|---|---|
| Distance | (D = S \times T) | “Speed × Time = Distance” |
| Speed | (S = \dfrac{D}{T}) | Divide distance by time |
| Time | (T = \dfrac{D}{S}) | Divide distance by speed |
| Average speed (multiple legs) | (S_{\text{avg}} = \dfrac{\text{Total distance}}{\text{Total time}}) | Use total, not individual speeds |
| Unit check | Ensure all units match | Convert minutes to hours, km to m if needed |
Common Mistakes to Avoid
- Mixing up units (e.g., using km/h for distance).
- Forgetting to convert minutes to hours before using the formula.
- Using speed as if it were distance (e.g., treating “12 km/h” as “12 km”).
- Ignoring that average speed is not the arithmetic mean of speeds when times differ.
Practice Tip:
Create a table with columns for Speed, Distance, and Time. Fill in two columns, solve for the third, and verify that all relationships hold. This visual approach helps cement the core formula and ensures unit consistency.