Time & Work • Topic 3 of 4

Pipes & Cisterns

A filling pipe is a positive rate, an emptying pipe (or leak) negative. Combine them by adding signed rates; net positive fills, net negative empties. The LCM method works: set tank capacity = LCM of the pipe times, give each pipe its units/min, then divide capacity by the net rate. Watch for a pipe opened later or a leak that slows a fill.

✅ Solved examples

1. Pipe A fills in 6 h, B in 4 h. Together?
LCM 12: rates 2+3=5/h; 12/5 = 2.4 h.
2. A fills in 10 h, leak empties in 15 h. Time to fill with leak?
Net 1/10 - 1/15 = 1/30 -> 30 h.
3. A fills in 12, B in 16; both open then A shut after 4 h. Time for B to finish?
LCM 48: rates 4+3=7; 4 h -> 28 units; 20 left at B (3/h) = 6.67 h more.
4. Two inlets 20 and 30 min, one outlet 60 min. All open — fill time?
LCM 60: 3 + 2 - 1 = 4 units/min; 60/4 = 15 min.

✏️ Practice — try these, take hints as needed

1. A in 8 h, B in 12 h. Together?
LCM 24: 3+2=5.
24/5.
—
4.8 h
2. Fill 9 h, leak empties 18 h. Net fill time?
1/9 - 1/18.
1/18.
—
18 h
3. Inlets 15 and 10 min. Together?
LCM 30: 2+3 = 5.
30/5.
—
6 min
4. Fill 5 h; outlet empties full tank 20 h. Both open?
1/5 - 1/20.
3/20.
20/3.
6.67 h
5. A in 6, B in 8, leak in 24 (h). All open?
LCM 24: 4+3-1 = 6.
24/6.
—
4 h

📝 Topic test — 8 questions

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