SOLUTION: Twenty men can finish the job in 30 days. Twenty five men were hired at the start and 10 quit after 20 days. How many days will it take to finish the job?

Question 735506: Twenty men can finish the job in 30 days. Twenty five men were hired at the start and 10 quit after 20 days. How many days will it take to finish the job?
Answer by josgarithmetic(39625) (Show Source): You can put this solution on YOUR website!
You need to determine the rate of work of 1 man. The rate should be in Jobs per Day or as Jobs per Number of Days.

If 20 men do the job in 30 days,
Then 1 man needs 20 times longer to do the job if working alone,
Which means 1 man does the job in 30*20 days,
Or
One man works at the rate of 1 job per 600 days.

We can use (rate)*(time)=(jobs), and the idea that men working together will ADD their rates through simple addition. Remember, now we know one man works at the rate of 1 job per 600 days.

Twenty-five men worked for 20 days. How much job was done?
The rate of 25 men would be , so the amount of work done in this time was job.

After 20 days, 10 men quit and the other 15 men stayed; so now, there be just 15 men to finish the job. The question is, how much time for these remaining 15 men to finish?

How much job must these 15 men do? job must these 15 men do. What is the work rate of these 15 men together? Their rate is jobs per day.

The time is calculable in , from which divide b.s. by r, . That would be for finding number of days to finish. Plug in all the numbers.

days, and be sure to simplify before doing the final computing.
(Looks like about days).
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