A pipe connected to a tank that fills it is called what?

An inlet. An inlet is a pipe that adds water into a tank. It raises the water level over time. The opposite kind of pipe is called an outlet. So the correct term here is inlet.

If a pipe can fill a tank in x hours, the part of the tank it fills in 1 hour is what?

1/x. The pipe fills 1 whole tank in x hours. Rate equals total work divided by total time. Total work here is 1 tank, and total time is x hours. So in 1 hour, it fills 1/x of the tank.

If an inlet fills a tank in x hours and an outlet empties it in y hours (with y greater than x), opening both together gives what net rate of filling per hour?

1/x - 1/y. The inlet's rate is 1/x tank per hour. The outlet's rate is 1/y tank per hour. Since y is greater than x, the inlet is the faster pipe. Opposing rates subtract, not add. So the net rate is 1/x minus 1/y, and the tank fills.

A pipe can fill a tank in 15 hours. What fraction of the tank is filled in 3 hours?

1/5. The pipe's rate is 1/15 of the tank per hour. In 3 hours, it fills 3 x 1/15 = 3/15 of the tank. The greatest common factor of 3 and 15 is 3. Dividing numerator and denominator by 3 gives 1/5. So 1/5 of the tank is filled. Check: 1 x 15 = 15, and 5 x 3 = 15, equal as expected.

An inlet pipe can fill a tank in 9 hours, while an outlet pipe can empty the full tank in 10 hours. If both pipes are opened together on an empty tank, how long will it take to fill?

90 hours. Let the inlet fill 1/9 of the tank each hour. Let the outlet drain 1/10 of the tank each hour. They act in opposite directions, so their rates subtract. Net rate = 1/9 - 1/10. With common denominator 90, this is 10/90 - 9/90. That gives 1/90 tank per hour, since the inlet is faster. This reduces to 1/90 tank per hour. Time is the reciprocal of the rate: 90 hours. Check: 90 hours x 1/90 per hour = 1 whole tank filled.

Pipe A can fill a tank in 6 hours and pipe B in 12 hours. Both are opened together, but pipe B is closed after 2 hours. How long will pipe A take to fill the remaining part of the tank?

3 hours. Let pipe A fill 1/6 of the tank each hour. Let pipe B fill 1/12 of the tank each hour. Together their combined rate is 1/6 + 1/12 = 1/4 tank per hour. Both pipes run together for 2 hours. Work done together = 2 x 1/4 = 1/2 of the tank. Remaining work = 1 - 1/2 = 1/2 of the tank. Pipe A alone now works at 1/6 tank per hour. Time needed = 1/2 / (1/6) = 1/2 x 6 = 3 hours. Check: 2 hours together plus 3 hours of A alone completes exactly 1 tank.

Pipe A can fill a tank in 30 hours. Pipe A and pipe B together can fill it in 20 hours. How long would pipe B alone take to fill the tank?

60 hours. Let pipe A fill 1/30 of the tank each hour. Together, A and B fill 1/20 of the tank each hour. Rates add, so pipe B's rate is the combined rate minus A's rate. Pipe B's rate = 1/20 - 1/30. Using common denominator 600, this is 30/600 - 20/600. That gives 10/600 tank per hour for pipe B. This reduces to 1/60 tank per hour. Time is the reciprocal of the rate: 60 hours. Check: 1/30 + 1/60 = 1/20, which equals 1/20.

Pipe A can fill a tank in 15 hours and pipe B in 20 hours. Both are opened together, but pipe B is closed after 8 hours. How long will pipe A take to fill the remaining part of the tank?

1 hour. Let pipe A fill 1/15 of the tank each hour. Let pipe B fill 1/20 of the tank each hour. Together their combined rate is 1/15 + 1/20 = 7/60 tank per hour. Both pipes run together for 8 hours. Work done together = 8 x 7/60 = 14/15 of the tank. Remaining work = 1 - 14/15 = 1/15 of the tank. Pipe A alone now works at 1/15 tank per hour. Time needed = 1/15 / (1/15) = 1/15 x 15 = 1 hour. Check: 8 hours together plus 1 hour of A alone completes exactly 1 tank.

Pipes and Cisterns: Formulas, Shortcuts and Solved Examples

Pipes and cisterns questions turn tanks into fractions per hour.

This lesson gives each rule, the reason it works and seven worked examples. It also lists the traps that cost marks.

The idea in brief

Rate: 1 ÷ time.
Net rate: inlets minus outlets.
Time: 1 ÷ net rate.
Pipe closed early: add the work in each stage.
Leak: treat it as an outlet.

What Pipes and Cisterns Questions Ask

What are these questions about?

Pipes fill or empty a tank. You find how long a job takes, or how much is done in a given time.

It is the same idea as Time and Work. A tank is the work. A pipe is the worker.

What kinds of pipes are there?

An inlet fills the tank.
An outlet empties the tank.
A leak is an outlet you did not choose.

An inlet adds to the tank each hour. An outlet takes away. The net rate decides the time.

What is the unit of work?

One full tank is 1 unit. A pipe that fills it in x hours does 1/x of it in one hour.

So every question becomes fractions of one tank.

Check 1

An outlet pipe adds to the water in the tank.

Core Rules and Why They Work

How do I find the rate of one pipe?

Rate per hour = 1 ÷ time.

If a pipe fills a tank in x hours, it fills 1/x in one hour.

Why it works: if it fills the whole tank in x hours, each hour it fills the same part. Those x equal parts make 1.

How do I find the time with several pipes?

Net rate = sum of inlet rates − sum of outlet rates.Time = 1 ÷ net rate.

Why it works: all pipes work at the same time, so their rates add or subtract.

When a pipe stops, add the work done in each stage. The stages together make one tank.

How do I find the part filled in some hours?

Part filled = hours ÷ time to fill.

A pipe that fills in 15 hours fills 3/15 = 1/5 in 3 hours.

Why it works: each hour does 1/15, so 3 hours do 3 times that.

How do I find one pipe from the rest?

One pipe’s rate = combined rate − the other rate.

If A takes 30 hours and both take 20, B’s rate is 1/20 − 1/30 = 1/60.

Why it works: the combined rate is the sum of both rates. So subtracting gives the missing one.

Check 2

If two inlets fill in 6 and 12 hours, together they take 4 hours.

Seven Solved Examples

Easy, step by step: a pipe fills a tank in 12 hours. What part is filled in 5 hours?

Step 1: one hour fills 1/12.

Step 2: five hours fill 5 × 1/12.

The part filled is 5/12.

Easy, step by step: an inlet fills a tank in 9 hours and an outlet empties it in 10 hours. How long to fill with both open?

Step 1: the inlet rate is 1/9 and the outlet rate is 1/10.

Step 2: the net rate is 1/9 − 1/10 = 1/90.

Step 3: time = 1 ÷ 1/90 = 90.

It takes 90 hours.

Easy, step by step: pipes A and B fill a tank in 6 and 12 hours. How long do both take together?

Step 1: the rates are 1/6 and 1/12, or 2/12 and 1/12.

Step 2: add them to get 3/12 = 1/4.

Step 3: time = 4 hours.

Both take 4 hours.

Medium, step by step: A takes 6 hours and B takes 12 hours. Both open, but B closes after 2 hours. How long does A need for the rest?

Step 1: together they fill 1/4 per hour. In 2 hours that is 1/2.

Step 2: the remaining part is 1 − 1/2 = 1/2.

Step 3: A fills 1/6 per hour, so it needs 1/2 ÷ 1/6 = 3 hours.

A needs 3 hours.

Medium, step by step: A fills a tank in 30 hours. A and B together fill it in 20 hours. How long does B alone take?

Step 1: the combined rate is 1/20 and A’s rate is 1/30.

Step 2: B’s rate is 1/20 − 1/30 = 3/60 − 2/60 = 1/60.

Step 3: time = 60 hours.

B alone takes 60 hours.

Exam level, step by step: a pipe fills a tank in 6 hours, but a leak makes it take 8 hours. How long does the leak take to empty a full tank?

Step 1: the pipe’s rate is 1/6. The net rate is 1/8.

Step 2: the leak’s rate is 1/6 − 1/8 = 4/24 − 3/24 = 1/24.

Step 3: time = 24 hours.

The leak empties the tank in 24 hours.

Exam level, step by step: two inlets fill in 10 and 15 hours. An outlet empties in 30 hours. All three are open. How long to fill?

Step 1: write the rates over 30. They are 3/30, 2/30 and −1/30.

Step 2: the net rate is (3 + 2 − 1)/30 = 4/30 = 2/15.

Step 3: time = 15/2 = 7.5 hours.

It takes 7.5 hours.

Check 3

In example 7, the outlet is subtracted from the inlets.

Common Traps and Shortcuts

Which traps cost marks?

Adding an outlet rate instead of subtracting it.
Using hours instead of rates.
Forgetting that a closed pipe stops working.
Subtracting times, not rates.
Mixing minutes and hours.

Which shortcuts save time?

For two inlets, time = (x × y) ÷ (x + y).
For an inlet and outlet, time = (x × y) ÷ (y − x).
Use the LCM of the times as the tank size.
Check that the answer is not smaller than the quickest inlet.

What patterns come up in exams?

Five patterns repeat. Combined time, inlet and outlet, a pipe closed early, a missing pipe and a leak.

Each takes under two minutes once you write the rates.

How does the LCM trick work?

Pick a tank size equal to the LCM of the times. For 10, 15 and 30, take 30 units.

Then each pipe’s rate is a whole number: 3, 2 and −1 units per hour.

The net rate is 4 units per hour, so the time is 30 ÷ 4 = 7.5 hours.

Check 4

A leak acts like an extra outlet pipe.

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