Can you dig it?

Let's say it takes $N$ workers $N$ hours to dig $N$ ditches.

The more workers you have the lazier the workers become because the total number of ditches dug per hour will always be 1. If $N = 1$ , it takes 1 worker 1 hour to dig one ditch. If $N = 2$ , it takes 2 workers 2 hours to dig two ditches, and the digging rate would be $\frac{1}{2}$ ditches per worker per hour. If $N = 3$ , the rate will be $\frac{1}{3}$ ditches per worker per hour.

We can start to see a trend now: The digging rate per worker is the reciprocal of $N$ .

So if $N = 4$ the digging rate per worker is $\frac{1}{4}$ ditches per worker per hour. If we take only two of those workers, our combined digging rate is $2\times\frac{1}{4} = \frac{1}{2} =$ half a ditch per hour. If they dig at that rate, then they will be done with the ditches in $\boxed{4}$ hours.

diggin it