📚 Time‑Speed‑Distance – Quick & Easy Study Notes
(For the Madhya Pradesh Patwari / Lekhpal Quantitative Aptitude exam)
1️⃣ What Are the Three Things?
| Word | Simple idea | Everyday picture |
|---|---|---|
| Distance | How far something goes | A bus travels 40 km from town A to town B |
| Speed | How fast it goes | Your scooter’s speedometer reads 50 km/h |
| Time | How long it takes | The bus ride lasts 48 minutes |
2️⃣ The Basic Relationship
Distance = Speed × Time
Think of it like this:
- Speed tells you “how many units you cover every hour.”
- Time tells you “how many hours you travel.”
- Multiply them → “total units travelled.”
Why?
If you drive 50 km/h for 2 hours, you cover 50 × 2 = 100 km.
3️⃣ Easy Steps to Solve a Problem
- Read the problem carefully.
- Identify which value is missing: distance, speed, or time.
- Put the known numbers into the formula.
- Calculate.
- Check units (km, hours, etc.) – they should cancel properly.
4️⃣ Tiny Example
Problem:
A bicycle travels 30 km in 1.5 hours.
What is the average speed?
Solution:
- Unknown = speed
- Formula:
Speed = Distance ÷ Time Speed = 30 km ÷ 1.5 h = 20 km/h
Answer: 20 km/h
5️⃣ Quick Tips
| Tip | Why it Helps |
|---|---|
| Write units next to numbers. | Prevents mixing km with miles or minutes with hours. |
| Convert minutes to hours (divide by 60). | Keeps all units in hours for km/h. |
| Use a calculator for division. | Reduces arithmetic mistakes. |
| Check if the answer makes sense. | A train can’t travel 5 km in 10 minutes – that’s impossible. |
6️⃣ Mini Practice Problems
| # | Question | Hint |
|---|---|---|
| 1 | A car travels 120 km in 3 hours. What is its speed? | Speed = Distance ÷ Time |
| 2 | A train covers 250 km in 5 hours. How long will it take to cover 500 km at the same speed? | Time = Distance ÷ Speed |
| 3 | A person walks 8 km in 1.6 hours. What is the walking speed? | Speed = Distance ÷ Time |
| 4 | A bike travels 60 km in 2 hours. How far does it travel in 4 hours? | Distance = Speed × Time (first find speed) |
| 5 | A bus takes 90 minutes to travel 45 km. What is its speed in km/h? | Convert 90 min → 1.5 h |
7️⃣ Answers
| # | Answer |
|---|---|
| 1 | 40 km/h |
| 2 | 10 hours |
| 3 | 5 km/h |
| 4 | 120 km |
| 5 | 30 km/h |
8️⃣ Final Thought
Remember:
- Speed tells how fast
- Time tells how long
- Distance tells how far
Plug the known ones into Distance = Speed × Time (or its rearranged forms) and you’re done!
Happy studying! 🚀