CDS Mathematics · Time and Work

Pipes and Cisterns

Pipes are workers whose job is filling a tank; an outlet is a worker with a negative rate.

All Time and Work notes CDS Mathematics strategy

Why this matters

Six PYQs, one of them HARD. Treat each inlet as a positive rate and each outlet or leak as a negative one, add them, and use stages when a pipe is opened late or closed early — the same equation as work in stages.

Concept 1 of 1: Inlets, outlets and leaks

A tap that fills a tank in

n

hours adds

\tfrac1n

of it an hour; a drain that empties it in

m

hours removes

\tfrac1m

. The net rate is the sum with signs.

Definition

Inlet: $+\dfrac1n$ . Outlet or leak: $-\dfrac1m$ .
Net rate $=$ inlets $-$ outlets; time $= \dfrac1{\text{net rate}}$ .
Pipes opened or closed part-way: stages that add to $1$ tank.
Capacity from litres per minute: capacity $=$ net litres per minute $\times$ minutes.

Net rate

\dfrac1T = \dfrac1{n} - \dfrac1{m}

Worked example

A tap fills a tank in

4

hours; a leak empties it in

12

. How long does the tap take with the leak open?

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

CDS · 2017 · CDS (II) 2017 — Elementary Mathematics · Q39Moderate

Example 1 · Time and Work · Pipes and Cisterns

A tap can fill a tub in 10 hours. After opening the tap for 5 hours it was found that a small outlet at the bottom of the tub was open and watcr was leaking through it. It was then immediately closed. It took 7 hours to fill the tub after closing the outlet. What time will be taken by the outlet to empty the full tub of water ?

Subtract the outlet

An outlet works AGAINST the tap. A tap of

4

hours and a leak of

12

hours together take

6

hours, not the

3

hours that adding the rates would give.

Drill 5 more on inlets, outlets and leaks

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (1)

Inlets, outlets and leaks
Net rate
$\dfrac1T = \dfrac1{n} - \dfrac1{m}$

Watch out for (1)

Subtract the outlet
→ Inlets, outlets and leaks

Test yourself on Time and Work

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