Understanding the Slower Pipe's Filling Time

Ever find yourself staring at a math problem that just seems to twist your brain in knots? Well, if you’re gearing up for the Officer Aptitude Rating (OAR) test, you might come across a problem involving filling pipes. Let’s jump into a common example: two pipes fill a pool together in five hours. But here’s the kicker — how long would it take the slower pipe to fill the pool all by itself? Spoiler alert: the answer is 11.25 hours, but don’t worry, we’ll walk through the logic together.

So, how do we figure this out? It all comes down to rates. If both pipes fill the pool in five hours, that means together, they complete 1/5 of the pool each hour. Now, let’s break it down a bit more. We can label the rate of the faster pipe as Rf, and the slower one as Rs. The equation can be pretty simple:

Rf + Rs = 1/5

But we also need to think about how long it takes each pipe to fill the pool separately. Let’s name the time it takes the slower pipe to fill the pool by itself Ts. Therefore, we can express Rs (the rate of the slower pipe) like this:

Rs = 1/Ts

Now, plug that into our combined work rate equation. This gives us:

Rf + 1/Ts = 1/5

Keep up with me! Here’s where we get a bit crafty. If we assume the faster pipe fills the pool in 5 hours less time than the slower pipe (so Ts - 5), we’re starting to shape a clearer picture.

If we replace Rf in the equation, we’ll need to get to an answer for Ts. But the real magic happens when you realize that it’s easier than it seems. If we rearrange that equation and make the appropriate substitutions, we’ll eventually solve for Ts and come to find out it takes 11.25 hours for the slower pipe to do its job alone.

Why does this matter? Well, this type of problem teaches not just about rates but about the process of logical deduction. It’s about breaking down the problem step by step. You might run into something similar in your OAR test, where understanding rates, time, and relationships between different values becomes essential.

And hey, while we’re on the subject, isn’t math just a fascinating puzzle sometimes? Sure, it can be daunting, but these challenges just require a little practice and patience. Don’t underestimate the power of practice tests—they can transform how you tackle these problems on exam day.

So, keep at it! Whether you're trying to fill up your knowledge or a pool, remember that every little step—yes, even a math question about pipes—can lead you to success. And who knows? You might find connections in unexpected places. Plus, breaking down these questions will not just help in tackling the OAR, but in real life too when you’re planning a simple DIY project or calculating time for any task.

Ready to tackle more problems? Every question you solve sharpens those skills, and when you see that progress, it's like filling up a pool—eventually, you'll have it over the brim. Let's keep those brains working and those skills honed! The OAR test is just a stepping stone on your journey, so gear up and get ready for the challenge!