Maharashtra TET – Quantitative Aptitude
Topic: Time‑Speed‑Distance
Goal – Understand the basic concepts, memorize the key formulas, and master the procedure to solve TET‑style problems efficiently.
1. Simple Explanation
The Time‑Speed‑Distance (TSD) relationship is a fundamental concept in physics and everyday life.
It tells us how far an object moves (distance) when it travels at a constant speed for a given period of time.
- Speed = How fast an object is moving (units: km/hr, m/s, etc.)
- Time = Duration of the motion (units: hours, minutes, seconds, etc.)
- Distance = Total path covered (units: km, m, etc.)
The three quantities are linked by a single linear equation:
[ \boxed{ \text{Distance} = \text{Speed} \times \text{Time} } ]
All other TSD problems can be reduced to this basic formula by simple algebraic manipulation.
2. Key Points
| Concept | Definition | Typical Units | Notes for TET |
|---|---|---|---|
| Speed | Distance covered per unit time | km/hr, m/s | In TET problems, always use the unit that matches distance/time given. |
| Time | Duration of motion | hr, min, sec | Convert all times to the same unit before calculation. |
| Distance | Total path covered | km, m | Convert distance to same unit as speed if required. |
| Average Speed | Total distance ÷ total time | same as speed | Used when motion is not at constant speed. |
| Relative Speed | Speed of one object relative to another | same as speed | Eg. two trains moving towards each other: v1 + v2. |
| Conversion | 1 hr = 60 min; 1 min = 60 sec | – | Always convert to a common unit (usually hours for km/hr). |
| Direction/Vector | Not needed for scalar TET questions | – | TET focuses on magnitudes, not directions. |
Common Formula Rearrangements
| Want (solve for) | Formula |
|---|---|
| Speed | (\displaystyle v = \frac{d}{t}) |
| Time | (\displaystyle t = \frac{d}{v}) |
| Distance | (\displaystyle d = v \times t) |
Dealing with Mixed Units
- Convert all times to hours (if speed in km/hr).
- Example: 30 min = 0.5 hr, 45 min = 0.75 hr.
- Convert speeds to km/hr (if distance in km).
- Example: 15 m/s = (15 \times 3.6 = 54) km/hr.
Relative Speed Problems
- Towards each other: (v_{\text{rel}} = v_1 + v_2)
- Away from each other: (v_{\text{rel}} = |v_1 - v_2|)
- Same direction: (v_{\text{rel}} = |v_1 - v_2|) (slower behind, faster ahead)
3. Worked Example
Question
Two trains start from stations A and B, which are 240 km apart. Train‑A travels at 60 km/hr and Train‑B travels at 45 km/hr, both heading towards each other. After how many hours will they meet?
Step‑by‑Step Solution
-
Identify given data
- Distance between A & B : (d = 240) km
- Speed of Train‑A : (v_A = 60) km/hr
- Speed of Train‑B : (v_B = 45) km/hr
-
Compute relative speed
Since they move towards each other, relative speed (v_{\text{rel}} = v_A + v_B = 60 + 45 = 105) km/hr. -
Apply the TSD formula
[ t = \frac{d}{v_{\text{rel}}} = \frac{240}{105} ] -
Simplify the fraction
[ \frac{240}{105} = \frac{240 \div 15}{105 \div 15} = \frac{16}{7} \text{ hours} ] -
Convert to hours and minutes
[ \frac{16}{7} \text{ hr} = 2;\text{hr} + \frac{2}{7}\text{ hr} ] [ \frac{2}{7}\text{ hr} \times 60 \text{ min/hr} = \frac{120}{7} \text{ min} \approx 17.14 \text{ min} ] -
Answer
The trains will meet after 2 hours 17 minutes (approximately).
Quick Check
- Distance covered by Train‑A in 2.2857 hr:
(60 \times 2.2857 \approx 137.14) km - Distance covered by Train‑B in 2.2857 hr:
(45 \times 2.2857 \approx 102.86) km - Sum ≈ 240 km ✔️
4. Quick Revision Summary
| Point | Tip |
|---|---|
| Remember the core equation | Distance = Speed × Time – always the base. |
| Convert units first | Work in the same unit (usually hours for km/hr). |
| Use relative speed for moving objects | Add speeds when moving towards each other; subtract when one is faster in the same direction. |
| Check the answer dimensionally | Result should be in hours if time asked, km if distance asked, etc. |
| Practice with mixed units | Convert minutes to hours, m/s to km/hr, etc. |
| Keep a cheat‑sheet | Quick formulas for (t, v, d) and relative speed. |
| Read the problem carefully | Identify “towards”, “away”, “same direction” – they change the speed addition/subtraction. |
Quick Practice Problem
*A car travels from town X to Y, covering