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Thought-Process to Discover Knowledge

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Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

Read in the blogs more about the unique learning experience at nubtrek.continue
mathsCommercial ArithmeticsRate and Span

Pipes and Cistern

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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