Server Error

Server Not Reachable.

This may be due to your internet connection or the nubtrek server is offline.

Thought-Process to Discover Knowledge

Welcome to nubtrek.

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.
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.

click on the content to continue..

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)

slide-show version coming soon