📚 Time‑Speed‑Distance (T‑S‑D) – Quick & Simple Notes
(For the Puducherry Patwari / Lekhpal Quantitative Aptitude exam)
1️⃣ What Is It?
Time‑Speed‑Distance is just a shortcut for “How far to walk, how fast to run, or how long a trip will take?”
Think of it as a traffic light that helps you decide when to leave, how fast to go, and how far you’ll travel.
| What you know | What you want to know | Example |
|---|---|---|
| Distance (how far) | Time (how long) | “I’ll walk 5 km in 1 hour.” |
| Speed (how fast) | Distance | “I run at 8 km/h; how far will I go in 2 h?” |
| Time | Speed | “I need to get there in 30 min; how fast must I go?” |
2️⃣ Simple Formulas
All are one‑step calculations.
| Goal | Formula | What to put in |
|---|---|---|
| Distance | Distance = Speed × Time |
Speed (km/h or m/s) + Time (h or s) |
| Speed | Speed = Distance ÷ Time |
Distance (km or m) ÷ Time (h or s) |
| Time | Time = Distance ÷ Speed |
Distance (km or m) ÷ Speed (km/h or m/s) |
Tip: Keep units the same. Convert if needed (e.g., 60 km/h = 1 km/min).
3️⃣ Everyday Analogies
| Situation | How T‑S‑D Helps | Quick Think‑Aloud |
|---|---|---|
| Driving to a market | If you know you’ll drive 30 km at 60 km/h, the trip takes 0.5 h (30 min). | “Speed × Time = Distance” → 60 × 0.5 = 30 km. |
| Walking to school | You walk 4 km at 5 km/h. How long? | “Distance ÷ Speed = Time” → 4 ÷ 5 = 0.8 h (48 min). |
| Running a race | You want to finish 10 km in 1 hour. How fast? | “Distance ÷ Time = Speed” → 10 ÷ 1 = 10 km/h. |
4️⃣ Tiny Example
Problem:
A train travels 180 km. Its speed is 60 km/h.
How long does it take?
Solution:
- The formula we need:
Time = Distance ÷ Speed. - Plug in:
Time = 180 km ÷ 60 km/h = 3 h.
Answer: 3 hours.
5️⃣ Quick Practice Problems
Solve them with the formulas above.
(Answers are at the bottom)
- A cyclist covers 45 km in 3 h. What was his average speed?
- A bus needs 2 h 30 min to travel 120 km. What is its speed?
- A person walks 8 km at a speed of 4 km/h. How long did the walk take?
- A car travels at 80 km/h. How far will it go in 4 h?
- A train travels 250 km in 5 h. What is the time it would take to travel 400 km at the same speed?
6️⃣ Quick Answers
| # | Answer |
|---|---|
| 1 | 15 km/h |
| 2 | 80 km/h |
| 3 | 2 h |
| 4 | 320 km |
| 5 | 8 h |
7️⃣ Tips for the Exam
- Read carefully – the question tells you which of the three (T, S, D) is missing.
- Keep units consistent – convert minutes to hours (divide by 60) or km/h to m/s (multiply by 1000/3600).
- Check the answer – if you get a speed of 200 km/h in a short distance, you’ve probably mis‑converted units.
- Use a calculator only for the final division/multiplication – the logic is simple.
- Practice “speed‑time‑distance” three‑step problems – they often appear as a twist of the basic formula.
8️⃣ Cheat‑Sheet (One‑Page Summary)
| Want | Formula | Quick Check |
|---|---|---|
| Distance | D = S × T |
Speed × Time = Distance |
| Speed | S = D ÷ T |
Distance ÷ Time = Speed |
| Time | T = D ÷ S |
Distance ÷ Speed = Time |
- Convert minutes to hours:
minutes ÷ 60 = hours. - Convert km/h to m/s:
km/h × (1000 m / 1 km) ÷ (3600 s / 1 h) = km/h × 0.2778. - Always double‑check: If something feels too fast or too slow, re‑look at your units.
🎯 Final Thought
Time‑Speed‑Distance is like a recipe:
- Distance = Speed × Time
- Speed = Distance ÷ Time
- Time = Distance ÷ Speed
Mix the right ingredient, and you’ll always get the answer! Good luck with your preparation!