maths > commercial-arithmetics

Pipes and Cistern

what you'll learn...

overview

An example to the rate $×$$\times$ span $=$$=$ aggregate, is
fill-rate $×$$\times$ time $=$$=$ amount-filled.

This is explained in detail for pipes and cisterns.

examples in pipe-custern

A pipe fills a cistern in $12$$12$ hours. The fill-rate of the pipe $=\frac{1}{12}$$= \frac{1}{12}$ cistern per hour.

Unitary method in pipe-cistern:
The volume filled in $1$$1$ unit time is the fill-rate.

A pipe fills a cistern in $12$$12$ hours.
The fill-rate of the pipe is $\frac{1}{12}$$\frac{1}{12}$ a cistern per hour.

A pipe fills at $\frac{1}{4}$$\frac{1}{4}$ cistern an hour. How long does it take to complete filling $3$$3$ cisterns?

Fill rate $=\frac{1}{4}$$= \frac{1}{4}$ of cistern
Volume filled $=3$$= 3$ cisterns
fill rate $×$$\times$ time $=$$=$ volume filled
time $=3÷\frac{1}{4}$$= 3 \div \frac{1}{4}$ $=12$$= 12$ hours

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

fill rate $×$$\times$ time $=$$=$ volume filled

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

The volume $=\frac{3}{4}×12=9$$= \frac{3}{4} \times 12 = 9$ cisterns.

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

fill rate $×$$\times$ time $=$$=$ volume filled
fill rate and fill volume are in direct variation.

The number of cisterns $=3÷\frac{1}{12}×\frac{1}{9}=4$$= 3 \div \frac{1}{12} \times \frac{1}{9} = 4$

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

fill rate $×$$\times$ time $=$$=$ volume filled
time and fill volume are in direct variation.

The time $=\frac{15}{3}×5=25$$= \frac{15}{3} \times 5 = 25$ hours.

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

fill rate $×$$\times$ time to fill $=$$=$ volume filled
fill rate and time are in inverse variation.

The time = $\frac{1}{4}×8÷1=2$$\frac{1}{4} \times 8 \div 1 = 2$ hours

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

Fill rate of first pipe $=\frac{3}{20}$$= \frac{3}{20}$
fill rate of second pipe $=\frac{2}{15}$$= \frac{2}{15}$

Combined fill rate of the two pipes
$=\frac{3}{20}+\frac{2}{15}$$= \frac{3}{20} + \frac{2}{15}$
$=\frac{9+8}{60}$$= \frac{9 + 8}{60}$
$=\frac{17}{60}$$= \frac{17}{60}$

fillrate $×$$\times$ time $=$$=$ volume
$\frac{17}{60}×$$\frac{17}{60} \times$ time = $17$$17$
time $=17÷\frac{17}{60}$$= 17 \div \frac{17}{60}$
$=60$$= 60$ hours

summary

Problems in Pipe-Cistern : Simplify the problem to
fill rate $×$$\times$ time $=$$=$ 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)

Outline