### Time and Work

Calculation of work done in a time:

If A does a task in 3 days and B does a task in 4 days. The in one day A does 1/3 work and B does 1/4 work.

Both working together do: ( 1 / 3 ) + ( 1 / 4 ) = ( 7 / 12 ) work. Thus the work requires 12 / 7 days to be completed when both work together.

Calculation of negative work done in a time:

If A builds a wall in 3 days and B builds a wall in 4 days, C breaks a wall in 12 days. The in one day A does 1/3 work and B does 1/4 work.

Total work done in a day = ( 1 / 3 ) + ( 1 / 4 ) – ( 1 / 12 ) = 6/12 = 1/2

Total days to build a wall = 2 days.

Work equivalence method / Calculation to solve time and work problems:

In such problems, concept of man-days is important. Example: If a contractor hires 50 workers to complete a road in 100 days. Then he finds out that in 50 days only 40% of road building is done. So how many more days shall he need to complete the road. How many more men would he need to build his road on time.

Case – I

Here 40% work is done in 50 days so 60% work shall be completed in ‘x’ days. By cross multiplying we get x as 75 days.

Case – II

But if work has to be completed on time then find the man-days. So 40% of the work took 50 men * 50 days = 2500 man-days. Then to complete 60% work lets assume ‘X’ man-days. So we get ‘X’ as 3750 man-days. But days are fixed as 50 so 3750 / 50 = 75 men are needed to finish job on time.

Equating men, women and work:

Suppose 8 men can do a job in 12 days and 20 women can do a job in 10 days. In how many days can 12 men and 15 women do the job.

For solving this again we need concept of man-days:

Work needs = 12 * 8 = 96 man-day or 20*10 = 200 woman-days.

But since work is same quantity we equate both:

96 man-days = 200 woman-days

1 man-day = 2.083 woman-day

Therefore in 1 day, 12 men = 12 * 2.083 = 25 women.

Hence 25+15 women = 40 women work on a job that takes 200 woman-days to complete. So to complete task we need 200 woman-days / 40 woman = 5 days.

### Problems on Trains and Poles

Calculating time to pass a pole or man who is stationary:

Time taken by a train of length X metres to pass a pole or a standing man or a signal  post is equal to the time taken by the train to cover X metres.

Calculating time to pass a object that has a width:

Calculating time to pass a train moving in same direction:

Suppose two trains or two bodies are moving in the same direction at A m / s and B m/s, where A > B, then their relatives speed = (A – B) m / s.

If two trains of length  a metres and b metres are moving in the same direction at u m  / s and v m  / s,  then  the  time  taken by  the faster    train  to cross  the slower train = (a+b)/(u-v) sec.

Calculating time to pass a train moving in opposite direction:

Suppose two trains or two bodies are moving in opposite directions at A m / s and B m/s, then their relative speed is = (A + B) m/s.

If two trains of length a metres and b metres are moving in opposite directions at u  m / s and v m/s, then time taken by the trains to cross each other =  (a + b)/(u+v) sec.

Calculating time to reach respective destinations after crossing each other

If two trains (or bodies) start at the same time from points A and B towards each other  and  after  crossing  they  take  a  and b  sec  in  reaching B  and A  respectively, then

(A’s speed ) : (B’s speed) = (b^1/2: a^1/2)

Practice Exercise: Time, Speed, Distance