Time and Distance
Speed, relative motion, average speed
Time, Speed and Distance is a fundamental topic in quantitative aptitude that deals with the relationship between three quantities: time taken, speed maintained, and distance covered. These problems appear frequently in competitive exams and require understanding of basic formulas, unit conversions, and various scenarios like relative speed, average speed, and meeting points.
Key formulas and rules
Key concepts
Basic Relationships
The three fundamental quantities are related by Speed = Distance/Time. If any two are known, the third can be calculated. Always ensure units are consistent—convert km/hr to m/s when working with meters and seconds, or vice versa using the conversion factors 5/18 and 18/5.
Average Speed
Average speed is always Total Distance divided by Total Time, NOT the arithmetic mean of speeds. For equal distances traveled at different speeds, use the harmonic mean formula: 2xy/(x+y). For different distances, calculate total distance and total time separately.
Relative Speed
When two bodies move in the same direction, their relative speed is the difference of their speeds. When moving in opposite directions, their relative speed is the sum of their speeds. This concept is crucial for problems involving trains, races, and meeting points.