Time and Work ( Concept of Negative work )

Concept of Negative Work

            

In this case one person works but another destroys it or cancels it. For example arun can write 20 pages per hour but his younger sister aruna erases 10 pages per hour which arun writes.

           

It means finally arun writes 10 pages per hour since each hour his sister earses 10 pages out of 20 written pages. Taken another example:

Problem:

            A tub can be filled in 20 minutes but there is a leakage in it which can empty the full tub in 60 minutes. In how many minutes it can be filled?

Solution:

Filling efficiency = 5%                       ( therefore 5 = 100/20)

Emptying efficiency = 1.66%             (therefore 1.66% =  100/60)

Net efficiency = 5 – 1.66 = 3.33%

Required time to fill the tub = 100/3.33 = 30 minutes

Alternatively:

In 1 minutes tub is filling = 1/20

In 1 minute tub is emptying = 1/60

In 1 minute, effective filling of tub = 1/20-1/60

                                                = 2/60 = 1/30

Since 1/30 part of tub is filled in 1 minute.

Therefore complete tub will be filled in 1/1/30 = 30 minutes