Patwari Exam · Reasoning
Time & Work, Speed-Distance-Time
This note explains combined work, speed-distance-time, average speed, and relative-speed train questions.
- Reasoning & Numerical Ability
- 5 min read
Verified 6 October 2026
Key Formulas & Methods
- Work-time basics
- Work-time: if A does a job in n days → A's one day's work = 1/n.
- Combined work formula
- A+B together: 1/n + 1/m = 1/d → d = nm/(n+m).
- Speed-distance-time
- Speed = distance/time; distance = speed × time; time = distance/speed.
- Average speed
- Average speed (equal distance) = 2ab/(a+b) where a, b are the two speeds.
- Train crossing
- Train questions: time to cross a point = length of train/speed.
- Relative speed (trains)
- Two trains: same direction → relative speed = speed₁ − speed₂; opposite directions → speed₁ + speed₂.
- Worked example
- Exam example: A does a job in 6 days, B in 12 days → together = 6×12/(6+12) = 4 days.
Frequently Asked Questions
How do you find the time when two people work together?+
If A does a job in n days and B in m days, together they will finish in d = nm/(n+m) days; e.g. if A takes 6 days and B takes 12 days, together they finish in 6×12/(6+12) = 4 days.
What is the relationship between speed, distance and time?+
Speed = distance/time, distance = speed × time, and time = distance/speed.
How is the relative speed of two trains found?+
If both trains travel in the same direction, relative speed = speed₁ − speed₂, and if they travel in opposite directions, relative speed = speed₁ + speed₂.