Speed, Distance & Time
Learning Objectives
- Understand the fundamental concepts of Speed, Distance & Time
- Apply key formulas and techniques to solve problems
- Practice with exam-level questions to build speed and accuracy
Key Concepts
What is Speed, Distance & Time?
Speed, distance, and time problems form a crucial part of SSC CGL Tier 1 quant. The basic relationship is Distance = Speed * Time. Problems involve trains, boats & streams, circular tracks, and meeting/overlap situations.
Key Concepts
1. Basic Formula: Speed = Distance / Time. A speed of 1 m/s = 18/5 km/h. Conversely, 1 km/h = 5/18 m/s. Always convert units when comparing.
2. Average Speed: When a body travels at speeds a and b for equal distances, average speed = 2ab/(a+b). When traveling for equal times, average speed = (a+b)/2.
3. Relative Speed: Two bodies moving towards each other have relative speed = sum of their speeds. Moving in the same direction, relative speed = difference of speeds. Time to meet = Distance / Relative Speed.
4. Train Problems: When a train passes a pole, distance = length of train. When it passes a platform, distance = length of train + length of platform. When two trains cross each other, relative speed and combined length are used.
5. Boats & Streams: Downstream speed = Boat speed + Stream speed. Upstream speed = Boat speed - Stream speed. Boat speed = (Downstream + Upstream)/2. Stream speed = (Downstream - Upstream)/2.
Solved Examples
a) 48 km/h b) 50 km/h c) 52 km/h d) 45 km/h
a) 60 km/h b) 72 km/h c) 80 km/h d) 90 km/h
a) 4 h b) 5 h c) 6 h d) 7.5 h
Shortcut Techniques
- When converting m/s to km/h, multiply by 18/5. When converting km/h to m/s, multiply by 5/18.
- For meeting/overlap problems, use relative speed. Time to meet = initial distance / relative speed.
- For circular track meetings, time to first meeting = circumference / relative speed.
- In boat-stream problems, if the boat covers the same distance upstream and downstream, average speed = (downstream * upstream) / boat speed.
Advanced Applications
Modern exams feature questions combining multiple quantitative concepts. Master these by practicing previous year papers.
Shortcut Methods
Percentages: Use fraction table (12.5%=1/8, 20%=1/5, 25%=1/4). SI/CI: For 2 years, CI-SI = P(r/100)^2. Time Work: Use LCM of time periods. Average Speed: 2ab/(a+b) for equal distances.
Advanced Applications
Modern exams feature questions combining multiple quantitative concepts. Master these by practicing previous year papers.
Shortcut Methods
Percentages: Use fraction table (12.5%=1/8, 20%=1/5, 25%=1/4). SI/CI: For 2 years, CI-SI = P(r/100)^2. Time Work: Use LCM of time periods. Average Speed: 2ab/(a+b) for equal distances.
Advanced Applications
Modern exams feature questions combining multiple quantitative concepts. Master these by practicing previous year papers.
Shortcut Methods
Percentages: Use fraction table (12.5%=1/8, 20%=1/5, 25%=1/4). SI/CI: For 2 years, CI-SI = P(r/100)^2. Time Work: Use LCM of time periods. Average Speed: 2ab/(a+b) for equal distances.
Advanced Applications
Modern exams feature questions combining multiple quantitative concepts. Master these by practicing previous year papers.
Shortcut Methods
Percentages: Use fraction table (12.5%=1/8, 20%=1/5, 25%=1/4). SI/CI: For 2 years, CI-SI = P(r/100)^2. Time Work: Use LCM of time periods. Average Speed: 2ab/(a+b) for equal distances.