Goa PSC – Quantitative Aptitude
Topic: Time – Speed – Distance
Goal: Master the basic relationship between Time, Speed, and Distance, solve typical PSC problems, and quickly revise the key formulas.
1. Simple Explanation
| Quantity | Symbol | Meaning | Units |
|---|---|---|---|
| Distance | d | Total ground covered | km, m, km/h‑hr |
| Speed | s | Rate of covering distance | km/h, m/s |
| Time | t | Duration of travel | h, min |
Fundamental Relation
[ \boxed{d = s \times t} ]
- If you know any two of the variables, you can find the third by rearranging the equation.
For Multiple Segments
-
Average Speed
[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} ] -
Time to Meet (two moving objects)
[ t_{\text{meet}} = \frac{\text{Initial Separation}}{\text{Relative Speed}} ]
2. Key Points
| # | Concept | How to Use | Common Pitfalls |
|---|---|---|---|
| 1 | Consistent Units | Always use the same units (e.g., km & h). | Mixing km and m or h and min leads to wrong answers. |
| 2 | Direction Matters | For relative speed, add speeds when objects move toward each other; subtract when in same direction. | Forgetting to subtract when moving same direction. |
| 3 | Average Speed vs. Arithmetic Mean | Average speed = total distance / total time, not (s₁ + s₂)/2. | Assuming average speed is the arithmetic mean of speeds. |
| 4 | Changing Speeds | Break the journey into segments, compute time for each, sum times. | Ignoring different speeds for different segments. |
| 5 | Time = Distance / Speed | Rearrange ( d = s t ) to ( t = d/s ). | Using ( t = s/d ). |
| 6 | Speed = Distance / Time | Rearrange to ( s = d/t ). | Using ( s = t/d ). |
3. Formulas (Quick Reference)
| Formula | Use | Example |
|---|---|---|
| (d = s \times t) | Distance from speed & time | (d = 60 \text{ km/h} \times 3 \text{ h} = 180\text{ km}) |
| (s = \dfrac{d}{t}) | Speed from distance & time | (s = \dfrac{120\text{ km}}{2\text{ h}} = 60\text{ km/h}) |
| (t = \dfrac{d}{s}) | Time from distance & speed | (t = \dfrac{150\text{ km}}{50\text{ km/h}} = 3\text{ h}) |
| (t_{\text{meet}} = \dfrac{D}{s_1 + s_2}) | Meeting time (opposite directions) | If (D=300\text{ km}), (s_1=50), (s_2=70) → (t_{\text{meet}}=2.5\text{ h}) |
| (t_{\text{meet}} = \dfrac{D}{ | s_1 - s_2 | }) |
| Average speed | (\displaystyle v_{\text{avg}} = \frac{\text{Total } d}{\text{Total } t}) |
4. Worked Example
Problem (Goa PSC style)
Two trains start simultaneously from stations A and B, 480 km apart.
Train‑A departs from A toward B at 80 km/h.
Train‑B departs from B toward A at 60 km/h.
Questions
- When will they meet?
- How far from station A will they meet?
Solution
-
Relative Speed
Since they are moving toward each other:
[ s_{\text{rel}} = 80 + 60 = 140 \text{ km/h} ] -
Time to Meet
[ t = \frac{\text{Distance}}{\text{Relative Speed}} = \frac{480}{140} = 3.\over