Algebra Work Problem

Question

A certain construction job could be finished in 150 days, if 50 men are working full time. 60 men started working on the job and after 20 days, 20 more men are added. But after 80 days 50 men quit the job. How long could it take for them to finish the job? choices are: A. 120 B. 130 C. 110 D. 100

Answer 1

We need 50 men who work 150 days, so a total of 7500 days. We know that 60 people work on it for 20 days, then 80 people work on it for 60 days, and then there are 30 people left. Calculating the remainder of days to finish the project, we get:

$$\frac{7500 - 60 \cdot 20 - 80 \cdot 60}{30} = \frac{1500}{30} = 50$$

In total, you need $20 + 60 + 50 = 130$ days to finish the project.

Answer 2

In a way this is more of a physics problem since The main issue is realizing what are the units that you will feel comfortable working with. Personally I took 1 to be the amount of work that 1 worker give during a day of work. Once you think of that as your unit you will want to convert your given information with something more useful. We don't really care how many days of work 50 workers need, rather we would like to know how meany day's of work it will take for one worker to complete the job: that is 150*50 = 7500 working day's.

After you have all of your information in order like that all you need to do is slowly sum up the amount of working days given (notice that the 80 man only work for 50 day's I totally got confused there). At that point you will get to the ending of the first 80 day's, you will know how many more working days are needed and how many workers will be working. That should be an easy enough problem to solve.

Finally you will know how many days it took for the'm 30 man to finish the remainder of the work, that plus the initial 80 days will give you the right answer.

Good luck.