The final variation of work/rate problems involves people or things Working Against Each Other. In cases such as these, you don't add the rates, but rather find the difference.

Example

One pipe is filling up a pool at $3$ liters per second. Unfortunately, the pool has a leak and water is leaking at a rate of $1$ liter per second. If the pool is $5000$ liters, how many minutes would it take to fill the pool?

In this case, the pipe and the leak are working AGAINST each other, so don't add the rates. Find the difference:

$$3 - 1 = 2$$

So the "relative" rate is $2$ liters per second, and we can use this value to solve.

$$5000 = 2t$$

$$t = 2500 \textrm{ seconds}$$

But don't forget to convert to minutes!

$$\frac{2500}{60} = 41.66 \textrm{ minutes}$$

Approximately.