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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

### Time and Work

An example to the rate xx span = aggregate, is
work-ratexx time = work-done.

This is explained in detail.

click on the content to continue..

A person completes a building in 12 days. What is her work rate?

• 30 days per month
• 1/12 of a building per day
• 1/12 of a building per day

The answer is "1/12 of a building per day".

Unitary method in time-work:
The work completed in 1 unit time is the work-rate.

A person completes a building in 12 days.
The work-rate of the person is 1/12 of a building per day.

A person works at 1/20 building per day. How long does the person take to complete 3 buildings?

• 60 days
• 60 days
• 20 days

The answer is "60 days"

work rate xx time = work done
Work-rate and work done are given. Time is to be calculated.

A person works at 1/22 building per day. How many buildings he would have completed in 77 days?

• 7 buildings
• 3.5 buildings
• 3.5 buildings

The answer is "3.5 buildings"

work rate xx time = work done
Work-rate and time are given. Work done is to be calculated.

A person completes 2 buildings in 30 days. How many buildings she would have completed if she works for 75 days?

• 5 buildings
• 5 buildings
• 7 buildings

The answer is "5 buildings"

work rate xx time = work done
Time and work done are in direct variation.

A person completes a building at 1/35 building per day and completes 2 buildings in a given time. If the work-rate is increased to 1/7 building per day, how many buildings would he complete?

• 10 buildings
• 10 buildings
• 1/5 buildings

The answer is "10 buildings"

work rate xx time = work done
work rate and work done are in direct variation.

A person completes 1/40 of a building per day and takes 120 days to complete a set of buildings. If the work rate is increased to 1/30, how many days does he take to complete the same?

• 90 days
• 90 days
• 120 days

The answer is "90 days"

work rate xx time = work done
work rate and time are in inverse variation.

Person A takes 40 days to complete 2 buildings and person B takes 30 days to complete 1 building. If they work together, how many days do they take to complete 5 buildings?

• 50 days
• 60 days
• 60 days

The answer is "60 days".

work rate of Person A = 2/40 = 1/20

work rate of person B = 1/30

If they work together, the combined work rate
= 1/20 + 1/30
=5/60
=1/12

workrate xx time = work
1/12 xx  time = 5 buildings
time =5 xx 12/1
=60 days.

Problems in Time-Work : Simplify the problem to
work rate xx time rArr work done

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

•  two are given, and the third is asked.

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

slide-show version coming soon