| Rule No. | Condition / Scenario | Formula / Definition |
| 1 | Inlet | A pipe that fills a tank. |
| – | Outlet | A pipe that empties a tank. |
| 2 | If a pipe fills a tank in $x$ hours | Part filled in 1 hour = $\frac{1}{x}$ |
| 3 | If a pipe empties a tank in $y$ hours | Part emptied in 1 hour = $\frac{1}{y}$ |
| 4 | Both pipes open (Filling > Emptying) | If $y > x$, Net part filled in 1 hour = $(\frac{1}{x} – \frac{1}{y})$ |
| 5 | Both pipes open (Emptying > Filling) | If $x > y$, Net part emptied in 1 hour = $(\frac{1}{y} – \frac{1}{x})$ |
Pipes and Cistern Formulas
| Rule No. | Condition / Scenario | Formula / Definition |
| 1 | Inlet | A pipe that fills a tank. |
| – | Outlet | A pipe that empties a tank. |
| 2 | If a pipe fills a tank in $x$ hours | Part filled in 1 hour = $\frac{1}{x}$ |
| 3 | If a pipe empties a tank in $y$ hours | Part emptied in 1 hour = $\frac{1}{y}$ |
| 4 | Both pipes open (Filling > Emptying) | If $y > x$, Net part filled in 1 hour = $(\frac{1}{x} – \frac{1}{y})$ |
| 5 | Both pipes open (Emptying > Filling) | If $x > y$, Net part emptied in 1 hour = $(\frac{1}{y} – \frac{1}{x})$ |
Key Terms to Remember:
- Inlet: Think of this as “positive” work (adding water).
- Outlet: Think of this as “negative” work (removing water).
- Net Work: The result of both pipes operating simultaneously.
