Work And Time

Concept #1.- Work done
If a person ‘A’ can do a work in ‘n’ days, then A’s 1 day’s work will be = 1/n Example. If a person ‘A’ can do a work in 4 days, then A’s 1 day’s work = ¼
So, No. of days = total work / work done in 1 day

Complete time = 1/ 1 day's Work


Concept #2. – Part of Work Done :

If A’s 1 day’s Work = 1/n, then after X days, A’s work = x (1/n)
If A’s 1 day’s work = 1/6, then after 3 days, A’s work = 3(1/6)

Part of work done = No. of days worked * 1 day's work = No. of days worked / Complete time

Concept #3. – Combined 1 Days Work :
When more than one person are working on the same job, then their combined 1 day’s work = sum of 1 day’s work for each person.

Example.- If A can do a job in ‘n’ days and B can do it in ‘m’ days and both A and B together can do it in ‘T’ days, then
A’s 1 day’s work = 1/n, B’s 1 days work = 1/m
(A+B)’s combined 1 day’s work = 1/T (concept -2) = A’s 1 day’s work + B’s 1 day’s work 1

1/ T = 1/M + 1/N

T = M * N / M+N

Similarly, if A,B and C are working on a work, then (A+B+C)’s 1 day work = A’s 1 day’s work + B’s 1 day’s work + C’s 1 day’s work.
?B’s 1 day’s work = (A+B+C)’s 1 day’s work – A’s 1 day’s work – C’s 1 day’s work.

Concept #4. – Comparison of Two Worker’s Rate:
If a person A is ‘n’ time as good workman as another person B, then Complete time by A/ = 1/n And after any time, A’s work /B’s work = n





Concept #5.
Chain Rule: (Man 1 * Day 1 * Work rate 1)/Amount of work done 1 = (Man 2 * Day 2 * Work rate 2) / Amount of work done 2

So from the chain rule we can make the following relationship:

1. Relationship between Men and Work.
More men ==========? can do ==========? More work
Less men ===========? can do =========? Less work

2. Relationship between Work and Time
More work ==========? takes ==========? More Time
Less work ===========? takes ==========? Less Time

3. Relationship between Men and Time
More men ===========? can do in =======? Less Time
Less men ============? can do in =======? More Time

Additional Concepts:
1. If A is twice as good as worker B, then A’s 1 day’s work / B’s 1 day’s work = 2/1, A’s time/B’s time = ½

2. If x men can do a job in t1 days and y man in t2 days, then (p men + q women) can do the work in 1/(p/xt1 + q/yt2) days.
Time = 1 / [(p/x * t1) + (q / y*t2)] days

3. x men or y women can do a work in t days, then (p men + q women) can do the same work in t/(p/x + q/y) days.
Time = T / (p/x + q/y) days

4. If a person A can do a work in ‘n’ days and A+B together can do it in ‘T’ days, then B alone can finished the work = T * n / n-T days.
Time = T * n / n-T days