<p><a href="https://www.prepswift.com/quizzes/quiz/prepswift-working-against-each-other" target="_blank">Working Against Each Other Exercise</a></p><p>The final variation of work/rate problems involves people or things <span style="color:#27ae60;">Working Against Each Other</span>. In cases such as these, you don't add the rates, but rather find the difference. </p>
<p><strong><span style="color:#8e44ad;">Example</span></strong></p>
<p>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 <strong>minutes</strong> would it take to fill the pool. </p>
<p>In this case, the pipe and the leak are working AGAINST each other, so don't add the rates. Find the difference:</p>
<p>$$3 - 1 = 2$$</p>
<p>So the "relative" rate is $2$ liters per second, and we can use this value to solve.</p>
<p>$$5000 = 2t$$</p>
<p>$$t = 2500 \ seconds$$</p>
<p>But don't forget to convert to minutes!</p>
<p>$$\frac{2500}{60} = 416.6 \ minutes$$</p>
<p>Approximately.</p>