In-Depth: Time, Speed and Distance

CLAT Application & Relevance

Importance: Low to Medium. Direct complex questions are less frequent in the modern CLAT. However, this topic can form the basis of a short Data Interpretation caselet or be part of a larger problem. The underlying logic (Distance = Speed × Time) is broadly applicable in various scenarios.

How it's tested: Comparing travel times/speeds for different entities mentioned in a passage; problems involving relative speed (two entities moving towards/away from each other); basic problems on trains or boats (less common, but concepts like relative speed apply).

Section 1: Core Concepts & Formulas

This topic explores the relationship between the distance covered, the speed at which it is covered, and the time taken.

Fundamental Relationship

Distance = Speed × Time
Derived: Speed = Distance / Time
Derived: Time = Distance / Speed

Ensure units are consistent (e.g., if speed is in km/hr, distance should be in km and time in hours).

Key Concepts & Formulas

Unit Conversion:
- To convert km/hr to m/s: Multiply by 5/18. (e.g., 72 km/hr = 72 * 5/18 = 20 m/s)
- To convert m/s to km/hr: Multiply by 18/5.
Average Speed:
- If different distances are covered at different speeds: Total Distance / Total Time.
- If same distance is covered at two different speeds (S1 and S2): Average Speed = (2 * S1 * S2) / (S1 + S2).
Relative Speed: The speed of one object with respect to another.
- When two objects move in opposite directions (towards each other or away from each other), their relative speed is the sum of their individual speeds (S1 + S2).
- When two objects move in the same direction, their relative speed is the difference of their individual speeds (|S1 - S2|).
Trains:
- When a train crosses a pole/man: Distance = Length of the train.
- When a train crosses a platform/bridge/another train: Distance = Length of train 1 + Length of train 2 (or platform).

Section 2: Solved CLAT-Style Examples

Example 1: Basic Time, Speed & Distance from a Caselet

Passage Context: A legal reporter needs to travel from City A to City B, which are 360 km apart, to cover a breaking story. If the reporter drives at an average speed of 80 km/hr for the first 3 hours and then at a reduced speed due to traffic for the remaining journey.

Question: "What was the reporter's speed during the remaining journey if the total travel time was 5 hours?"

Detailed Solution:
1. Distance covered in first 3 hours: Distance = Speed × Time = 80 km/hr × 3 hours = 240 km.
2. Remaining Distance: Total Distance - Distance covered = 360 km - 240 km = 120 km.
3. Remaining Time: Total Time - Time in first part = 5 hours - 3 hours = 2 hours.
4. Speed during remaining journey: Speed = Remaining Distance / Remaining Time = 120 km / 2 hours = 60 km/hr.
Answer: The reporter's speed during the remaining journey was 60 km/hr.

Example 2: Relative Speed (Opposite Direction)

Passage Context: Two legal counsels, Mr. Sharma and Ms. Verma, are traveling from two different cities, P and Q, which are 750 km apart. Mr. Sharma starts from P towards Q at 70 km/hr, and Ms. Verma starts from Q towards P at 80 km/hr. They both start at the same time.

Question: "After how many hours will they meet?"

Detailed Solution:
1. Identify Speeds and Total Distance: Speed of Mr. Sharma (S1) = 70 km/hr Speed of Ms. Verma (S2) = 80 km/hr Total Distance = 750 km
2. Calculate Relative Speed (Opposite Direction): Relative Speed = S1 + S2 = 70 + 80 = 150 km/hr.
3. Calculate Time to Meet: Time = Total Distance / Relative Speed = 750 km / 150 km/hr = 5 hours.
Answer: They will meet after 5 hours.