📚 Time‑Speed‑Distance (TSD) – Study Notes
Why it matters:
The TSD concept appears in almost every quantitative aptitude test – from the Navy AA exam to SAT, GRE, GMAT, and everyday problem‑solving. Mastery of this topic gives you a reliable shortcut to tackle a wide variety of questions quickly and accurately.
1. Simple Explanation
| Symbol | Meaning | Units |
|---|---|---|
| (t) | Time | hours, minutes, seconds |
| (s) | Speed / Velocity | km/h, m/s, mph, etc. |
| (d) | Distance | km, m, miles |
The core relationship
[ \boxed{d = s \times t} ]
- Distance equals Speed multiplied by Time.
- Inverse forms:
- (s = \dfrac{d}{t})
- (t = \dfrac{d}{s})
Key insight: All three variables are linearly related. Changing one changes the others proportionally.
2. Key Points to Remember
| Category | Detail |
|---|---|
| Units | Keep all units consistent before plugging into the formula. |
| Direction | For speed (scalar) you ignore direction. For velocity (vector), direction matters, but most aptitude problems use speed. |
| Unit Conversion | Use 1 h = 60 min, 1 h = 3600 s, 1 mile ≈ 1.609 km, etc. |
| Common Tricky Situations | • 1 km = 1000 m • 1 hr = 60 min • 1 mile = 1.609 km |
| Multiple Speeds | When an object changes speed, split the journey into segments. |
| Average Speed | (\displaystyle \text{Avg speed} = \frac{\text{Total distance}}{\text{Total time}}) |
| Relative Speed | When two objects move towards/away from each other: (\displaystyle \text{Relative speed} = s_1 + s_2) (towards) or ( |
| Speed of Light / Sound | For special cases, use (c = 3\times 10^8,\text{m/s}) or (v_{\text{sound}} \approx 340,\text{m/s}). |
3. Problem‑Solving Strategy
- Read the question carefully. Identify which variable(s) are given and which are asked.
- Check units – convert everything to a single consistent set (usually SI: meters, seconds).
- Decide on the formula – choose the form of (d = s \times t) that directly gives the answer.
- Plug in the numbers – do the arithmetic. Keep track of sign/direction if needed.
- Verify – cross‑check units and sanity of the result (e.g., distance can’t be negative).
4. Worked Example
Problem
A naval ship sails from Port A to Port B at a constant speed of 20 km/h. The distance between the ports is 150 km.
Question: How long will the ship take to reach Port B?
Step 1: Identify variables
- (s = 20\ \text{km/h})
- (d = 150\ \text{km})
- Find (t).
Step 2: Use the formula
[ t = \frac{d}{s} = \frac{150\ \text{km}}{20\ \text{km/h}} ]
Step 3: Compute
[ t = 7.5\ \text{h} ]
Step 4: Convert if needed
(7.5\ \text{h} = 7\ \text{h}\ 30\ \text{min}).
Answer: 7 hours 30 minutes.
5. Quick Revision Summary
| Concept | Formula | Typical Use |
|---|---|---|
| Distance | (d = s \times t) | When speed & time known |
| Speed | (s = \dfrac{d}{t}) | When distance & time known |
| Time | (t = \dfrac{d}{s}) | When distance & speed known |
| Average Speed | (\displaystyle \frac{\text{Total } d}{\text{Total } t}) | Multiple segments |
| Relative Speed | (s_1 + s_2) (towards) | Two moving objects |
| Unit Conversion | 1 km = 1000 m, 1 h = 3600 s | Keep consistent |
6. Practice Problems (Try before checking)
- A submarine travels 240 km at 30 km/h. How many hours does it take?
- A ferry covers 120 m in 45 seconds. What is its speed in km/h?
- Two boats depart from the same dock heading in opposite directions. One travels at 15 km/h, the other at 10 km/h. After 3 hours, how far apart are they?
- A train travels 600 km in 5 hours. If it stops for 30 minutes, what is its average speed for the whole journey?
Hints: Use the formulas above and convert all units to km and h for consistency.
Final Tip
Memorize the core equation (d = s \times t). Once you have that, the rest is just a matter of plugging in the right numbers and keeping units straight. Happy practicing!