Suppose that the amount of time it takes to build a highway varies directly with the length of the highway and inversely with the number of workers. Suppose also that it takes 100 workers 69 weeks to build 4 miles of highway. How many workers would be needed to build 16 miles of highway in 15 weeks?
HELP PLEASE????

Question

Suppose that the amount of time it takes to build a highway varies directly with the length of the highway and inversely with the number of workers. Suppose also that it takes 100 workers 69 weeks to build 4 miles of highway. How many workers would be needed to build 16 miles of highway in 15 weeks? 
HELP PLEASE????

anonymous · Answer

I believe the answer is 1840 workers.

I was confused at first, but set up a simpler example that helped me evaluate the problem. Let's say there is a road built in 1 week by 1 worker that is 1 mile long. If you add one more worker, you divide the time by two because the time is inversely proportional to the number of workers. So then you have 0.5 weeks for 2 workers and 1 mile. I then set up a ratio:

|dw:1334209077216:dw|

As for why this is correct, I don't really have a good explanation, but I'm fairly certain this ratio also holds true for the numbers given in the problem. So set up 

(69/15)=(4/100)/(16/x)

Where x is the number of workers you're looking for. Then solve for x and you'll get 1840 workers.