Cfrgtkky

40 man working on a construction job had completed 1/3 of the jobs in the previous 15 days. The job was behind schedule, and needed to be completed 12 days from now. Additional workers needed to be hired an order to accomplish that. How many additional workers needed to be hired?

Your workers have contributed $15cdot 40 = 600$ man-days to the project.

This is $frac 13$ the required amount. The project requires $1800$ man*days.

You still need to apply $1200$ man*days

$frac {1200 text {man*days}}{12 text {days}} = 100$ men

or 60 additional men.

I think the answer is ( roll mouse over to reveal answer and working )

60 more workers

because

40 did 1/3 of the work in 15 days. so 2/3 of the work remains, which would take 80 workers 15 days, but it needs to be 12 days so we multiply by 5/4 and need total of 100 workers, which is 60 more. NB 5/4 is 15/12 - the 'speed up ratio' required to go from 15 days to 12 days.

Now....

This answer relies on everything being 'linear'. So the assumption that 80 workers get twice as much done per day as 40 workers is an assumption of linearity. In the real world, of course, problems are often non-linear. But I like this problem as it has several steps and twists along the way. Such as 1/3 of the work is already done and the way the question asks for the number of additional workers required.