📚 Time‑Speed‑Distance (TSD) – Study Notes
Program: Madhya Pradesh Patwari / Lekhpal
Subject: Quantitative Aptitude
Purpose: Quickly estimate the distance travelled, the time taken or the speed of an object when any two of the three quantities are known.
Formula:
[ \boxed{\text{Distance (D)} = \text{Speed (S)} \times \text{Time (T)}} ]
1️⃣ Simple Explanation
- Speed (S): Rate of motion, usually given in km/h, m/s, or mph.
- Time (T): Duration of motion, usually in hours, minutes, or seconds.
- Distance (D): Total path covered, usually in km, m, or miles.
The formula states that Distance = Speed × Time.
If any two of the variables are known, rearrange the formula to find the third.
| Known | Unknown | Formula |
|---|---|---|
| Speed & Time | Distance | D = S × T |
| Distance & Time | Speed | S = D ÷ T |
| Distance & Speed | Time | T = D ÷ S |
Tip: Convert units so that they match (e.g., hours to minutes, km to m) before applying the formula.
2️⃣ Key Points to Remember
| # | Point | Why It Matters |
|---|---|---|
| 1 | Unit Consistency | Wrong units give wrong answers. |
| 2 | Speed can be Average or Instantaneous | In these problems, speed is always average. |
| 3 | Time in Fractional Hours | 30 min = 0.5 h, 15 min = 0.25 h, etc. |
| 4 | Speed in m/s ↔ km/h | 1 km/h = 0.27778 m/s. Useful when converting. |
| 5 | Time = Distance ÷ Speed | Handy for problems asking “how long will it take?” |
| 6 | Distance = Speed × Time | Handy for “how far will it travel?” |
| 7 | Speed = Distance ÷ Time | Handy for “what is the speed?” |
| 8 | Use of Ratios | Many problems use “speed of train A to B is 3:2” etc. |
| 9 | Check for “average speed” vs “maximum speed” | In exams usually average. |
| 10 | Common Mistakes | Mixing up minutes and hours, forgetting to divide by 60, rounding errors. |
3️⃣ Worked Example
Problem:
A train travels from City‑A to City‑B at an average speed of 80 km/h.
If the distance between the two cities is 240 km, how long will the journey take?
Step‑by‑step Solution
-
Identify knowns and unknowns
- Speed, S = 80 km/h
- Distance, D = 240 km
- Time, T = ?
-
Choose the correct formula
[ T = \frac{D}{S} ] -
Plug in the values
[ T = \frac{240 \text{ km}}{80 \text{ km/h}} = 3 \text{ h} ] -
Answer
The train will take 3 hours to cover 240 km.
Quick Check
- Does 80 km/h × 3 h equal 240 km?
Yes, 80 × 3 = 240. ✔️
4️⃣ Another Example (Speed Calculation)
Problem:
A cyclist covers 45 km in 1.5 hours. Find his average speed in km/h.
Solution
[ S = \frac{D}{T} = \frac{45 \text{ km}}{1.5 \text{ h}} = 30 \text{ km/h} ]
Answer: 30 km/h.
5️⃣ Quick Revision Summary
- Formula: ( D = S \times T )
- Rearrangements:
- ( S = \frac{D}{T} )
- ( T = \frac{D}{S} )
- Unit Conversion:
- 1 h = 60 min, 1 km = 1000 m
- 1 km/h = 0.27778 m/s
- Common Pitfalls:
- Mixing hours/minutes
- Forgetting to divide minutes by 60 when converting to hours
- Using incorrect speed (instantaneous vs average)
- Rounding too early
Quick Self‑Check Questions
-
If a bus travels 120 km in 4 hours, what is its average speed?
Answer: 30 km/h -
A car covers 75 km at 50 km/h. How long did it take?
Answer: 1.5 h -
A train moves at 90 km/h. How far will it go in 2.5 hours?
Answer: 225 km
Tip for Exam:
Write down a small “TSD cheat sheet” on a sticky note:D = S × T S = D ÷ T T = D ÷ SKeep units in check and perform any necessary conversions before plugging numbers into the formula.
Good luck, and keep practicing! 🚀