Time – Speed – Distance (T‑S‑D)
Quantitative Aptitude – Mizoram Forest Guard
Time‑Speed‑Distance problems involve one or more of the three variables:
T – Time, S – Speed, D – Distance.
The basic relation that ties them together is
[ \boxed{D = S \times T} ]
1. Simple Explanation
| Variable | Meaning | Units (common) | How it’s used |
|---|---|---|---|
| T | Time taken to cover a distance | Hours, Minutes, Seconds | Multiply by speed to get distance |
| S | Speed (rate) at which something moves | km/h, m/s, km/min | Distance divided by time |
| D | Distance covered | km, m, miles | Speed multiplied by time |
Key Idea
If you know any two of the three, you can find the third by rearranging the basic formula.
2. Key Points & Tips
| # | Concept | Tip |
|---|---|---|
| 1 | Unit Consistency | Always convert units so they match (e.g., if speed is km/h, time must be in hours). |
| 2 | Speed Variations | “Average speed” = total distance / total time. If speeds differ (e.g., uphill vs downhill), use weighted averages or break into segments. |
| 3 | Relative Speed | When two objects move towards/away from each other, add/subtract their speeds. |
| 4 | Time Differences | If one person starts later, subtract the time lag from total time. |
| 5 | Distance Differences | If two objects start at different points, compute the difference in starting positions. |
| 6 | Common Phrases | “Cover a distance”, “travel a distance”, “move a distance” all mean the same. |
| 7 | Unit Conversion | 1 km = 1000 m; 1 hour = 60 min; 1 minute = 60 sec. |
| 8 | Practical Application | Forest guards often need to compute patrol routes, fuel needs, or travel times; accurate T‑S‑D calculations save resources. |
3. Worked Example
Scenario
A forest guard patrols a circular track of 12 km diameter. He walks 4 km along the perimeter, then rides a jeep for 8 km.
- Walking speed = 5 km/h
- Jeep speed = 32 km/h
Find the total time taken for the patrol.
Step‑by‑step
| Segment | Distance (km) | Speed (km/h) | Time (h) |
|---|---|---|---|
| Walking | 4 | 5 | ( \frac{4}{5} = 0.8 ) |
| Jeep | 8 | 32 | ( \frac{8}{32} = 0.25 ) |
Total time = (0.8 + 0.25 = 1.05) h
Convert to minutes: (1.05 \times 60 = 63) minutes.
Answer: The guard takes 63 minutes for the patrol.
4. Quick Revision Summary
- Formula: (D = S \times T)
- Rearrangements:
- (S = \dfrac{D}{T})
- (T = \dfrac{D}{S})
- Always check units first.
- For varying speeds, break the journey into segments.
- Average speed = total distance / total time.
- Relative speed = (S_{\text{A}} \pm S_{\text{B}}) (towards/away).
Practice Tip – Start each problem by listing the knowns and unknowns, select the appropriate formula, and solve systematically.
Good luck, Forest Guard! Keep your calculations clear and double‑check your units.