# How To Solve Work Problems In Math

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Visit Stack Exchange A project can be done by 70 men in 100 days.

If you can use this path, it will give you the solution fastest, though it is not as easy to follow as it seems. As it happened, instead of all of them working together to finish the job, they started working together, but at the end of every 10th day 5 men left. We will be clear about this boundary concept as we proceed.

1st 10 days, 40 men worked, work done = 400 mandays, 2nd 10 days, 35 men worked, work done = 350 mandays, 3rd 10 days, 30 men worked, work done = 300 mandays, 4th 10 days, 25 men worked, work done = 250 mandays, till now in 40 days 1300 mandays work is done, while total work is 1680 mandays.

There were 80 men at the start of the project but after 50 days, 20 of them had to be transferred to another project. I have encountered work problems before with the general formula $$\frac1A \frac1B \dots = \frac1T.$$ There's also problems with time involved: $$t_A\left(\frac1A \frac1B\right) t_B\left(\frac1C \frac1D\right) \dots = 1.$$ This problem incorporates people leaving, remaining days. Think about the required amount of work in man-days.

How long will it take the remaining workforce to complete the job? The project requires *100=7000$man-days of total work.While combining work of teams we can simply add the Work measures in mandays, boydays, womandays or whatever the case may be.A work can be completed by 12 men in 24 days and 12 women in 12 days.when we combine work of teams of different types of workers, for example, men and women.For men we will use, Mandays as work measure and for Women, Womandays.As time and worker number are inversely proportional, 3 men’s teams will complete the work in,$\displaystyle\frac=8\$ days.This approach is wholly conceptual and based on deductive reasoning (in this case, mathematical reasoning, which is a subset of deductive reasoning). Crossing over the last point, the nature of event changes.We can proceed safely to the 5th segment of 10 days.5th 10 days, 20 workers worked, work done = 200 mandays, till now total of 1500 mandays work done, work left is 180 mandays which will be worked upon by 15 men.Crossing this boundary, the full period is broken and job is finished in 3 more days. As 40 men working together all through take 42 days to complete the job, and in the second case, every 10 days worker force reduces by 5, we can safely test for 50 days work portion completion.This is called an with which the number of days can safely be multiplied.

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