An example to the rate `xx` span `=` aggregate, is

fill-rate `xx` time `= ` amount-filled.

This is explained in detail for pipes and cisterns.

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A pipe fills a cistern in `12` hours. What is the fill rate of the pipe?

- `12` hours per pipe
- `1/12` cistern per hour
- `1/12` cistern per hour

The answer is "`1/12` cistern per hour"

Unitary method in pipe-cistern:

The volume filled in `1` unit time is the fill-rate.

A pipe fills a cistern in `12` hours.

The fill-rate of the pipe is `1/12` a cistern per hour.

A pipe fills at `1/4` cistern an hour. How long does it take to complete filling `3` cisterns?

- `4` hours
- `12` hours
- `12` hours

The answer is "`12` hours".

Fill rate `= 1/4` of cistern

Volume filled `= 3` cisterns

fill rate `xx` time `= ` volume filled

time `= 3 -: 1/4` `=12` hours

A pipe fills `3` cisterns in `4` hours. How many cisterns would be filled by the pipe in `12` hours?

- `12` cisterns
- `9` cisterns
- `9` cisterns

The answer is "`9` cisterns".

fill rate `xx` time `= ` volume filled

Fill rate and time are given. Volume filled is calculated.

A pipe fills a cistern at `1/12` cistern per hour and fills `3` cisterns in a given time. If the fill-rate is increased to `1/9` cistern per hour, how many cisterns would be filled in the same time?

- `4` cisterns
- `4` cisterns
- `3` cisterns

The answer is "`4` cisterns".

fill rate `xx` time `= ` volume filled

fill rate and fill volume are in direct variation.

A pipe takes `15` hours to complete filling `3` cisterns. If the number of cisterns is increased to `5`, how much time does the pipe take to fill them?

- `25` cisterns
- `25` hours
- `25` hours

The answer is "`25` hours".

fill rate `xx` time `= ` volume filled

time and fill volume are in direct variation.

A pipe fills at `1/4` cistern per hour rate and take `8` hours to complete filling a number of cisterns. If the fill rate is increased to `1` cistern per hour, how much time does it take to fill the same number of cisterns?

- `2` cisterns
- `2` hours
- `2` hours

The answer is "`2` hours".

fill rate `xx` time to fill `= ` volume filled

fill rate and time are in inverse variation.

One pipe takes `20` hours to fill `3` cisterns and another pipe takes `15` hours to fill `2` cisterns. If these fill together, how much time do the pipes take to fill `17` cisterns?

- `60` hours
- `60` hours
- `120` hours

The answer is "`60` hours"

Fill rate of first pipe `= 3/20`

fill rate of second pipe `= 2/15`

Combined fill rate of the two pipes

`= 3/20 + 2/15`

` =(9+8)/60`

`= 17/60`

fillrate `xx` time `=` volume

`17/60 xx ` time = `17`

time `=17 -: 17/60`

`=60` hours .

**Problems in Pipe-Cistern** : Simplify the problem to *fill rate `xx` time `=` filled volume*

There are three quantities in the equation. Possible formulation of questions are

• two quantities are given, and the third is asked.

• two quantities are given. If one of the given is modified, the changed second is asked. (direct or inverse variation)

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