CSAT
Time, Speed and Work
CSAT
Time, Speed and Work — Quick Revision
One-page CSAT revision of time, speed, distance and work: unit ladder, average and relative speed, trains, boats, LCM work method, pipes and man-days.
SyllabusCSAT · Basic numeracy (numbers and their relations, orders of magnitude, etc.) — Class X level
All the rules for CSAT speed and work questions, on one page.
Unit Ladder
| km/h | 18 | 36 | 54 | 72 | 90 | 108 |
|---|---|---|---|---|---|---|
| m/s | 5 | 10 | 15 | 20 | 25 | 30 |
Speed, Distance, Time
| Situation | Formula |
|---|---|
| Basic | $D = S \times T$ |
| Average speed | Total distance ÷ total time |
| Equal distances at $x$, $y$ | $\dfrac{2xy}{x + y}$ |
| Equal times at $x$, $y$ | $\dfrac{x + y}{2}$ |
| Three equal distances at $x, y, z$ | $\dfrac{3}{\frac{1}{x} + \frac{1}{y} + \frac{1}{z}}$ |
| Opposite directions | Relative speed $= S_1 + S_2$ |
| Same direction | Relative speed $= \lvert S_1 - S_2 \rvert$ |
| Constant distance | Time ratio = inverse of speed ratio |
Trains, Boats
| Situation | Distance / formula |
|---|---|
| Train passes a pole | Own length $L$ |
| Train crosses platform $P$ | $L + P$ |
| Two trains cross | $L_1 + L_2$ at relative speed |
| Downstream / upstream | $b + s$ / $b - s$ |
| Boat / stream speed | $\dfrac{D + U}{2}$ / $\dfrac{D - U}{2}$ |
Work, Pipes, Man-Days
| Situation | Method |
|---|---|
| Total work | LCM of individual days |
| Efficiency | Total work ÷ days |
| Working together | Add efficiencies |
| Emptying pipe / leak | Subtract its efficiency |
| “A is $k$ times as efficient as B” | A takes $\dfrac{1}{k}$ of B’s time |
| Same job, different crews | $M_1 D_1 H_1 = M_2 D_2 H_2$ |
High-yield facts
- Equal-distance average speed is always below the simple mean (unless speeds are equal).
- Speed $\tfrac{3}{4}$ of usual → time $\tfrac{4}{3}$ of usual → extra time is $\tfrac{1}{3}$ of usual time.
- Together, A (12 days) and B (18 days) take 7.2 days — never add days.
Traps
Three classic errors
- Taking the simple average of two speeds over equal distances.
- Ignoring the train’s own length when it crosses a platform or another train.
- Mixing km/h and metres without converting.
Related Topics
- Time, Speed, Distance and Work
- Time, Speed and Work — practice questions
- Percentages, Ratio and Averages — quick revision
- All quick-revision sheets
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