Filling Time: How Long To Fill A 50-Liter Jug?

Hey guys! Ever wondered how long it takes to fill a container with water? Let's dive into a fun physics problem where we'll figure out just that. We're going to tackle a question about filling a jug with water from a fountain, and it's all about understanding rates and proportions. So, grab your thinking caps, and let's get started!

Understanding the Problem

Okay, so here's the deal: we know it takes 24 seconds to fill a 30-liter jug from a fountain. The big question is, how long will it take to fill a 50-liter jug from the same fountain? This is a classic problem that involves understanding the flow rate of the fountain and using that information to calculate the time it takes to fill a different volume. The key here is that the flow rate of the fountain is constant, meaning it delivers the same amount of water per second. This allows us to set up a proportion and solve for the unknown time. To really grasp this, let's break down the core concepts. We need to figure out the rate at which the fountain is filling the jug. This rate is usually expressed in liters per second. Once we know this, we can use it to calculate how long it will take to fill any volume, including our 50-liter jug. This involves a bit of basic algebra, but don't worry, we'll walk through it step by step. Think of it like this: if you know how fast your car is going (miles per hour), you can figure out how long it will take to reach your destination if you know the distance. This problem is essentially the same concept, just with water and liters instead of cars and miles! Now, let's get into the nitty-gritty of solving this problem. We'll start by calculating the flow rate, then use that to find the time it takes to fill the 50-liter jug. It's all about breaking down the problem into smaller, manageable steps. So, are you ready to become a water-filling whiz? Let's do it!

Calculating the Flow Rate

First things first, let's figure out the flow rate of the fountain. This is super important because it tells us how much water the fountain is dispensing per unit of time. In our case, we know it fills a 30-liter jug in 24 seconds. So, how do we find the flow rate? Simple! We divide the volume of water (30 liters) by the time it takes to fill it (24 seconds). This gives us the flow rate in liters per second. So, the calculation looks like this: Flow Rate = Volume / Time. Plugging in our numbers, we get: Flow Rate = 30 liters / 24 seconds. Now, let's do the math. 30 divided by 24 is 1.25. So, the flow rate of the fountain is 1.25 liters per second. This means that every second, the fountain dispenses 1.25 liters of water. This is a crucial piece of information because now we can use this flow rate to figure out how long it will take to fill any size container, including our 50-liter jug. Think of it like this: if you're filling a bathtub, you want to know how fast the water is coming out of the faucet. That's the flow rate! Once you know that, you can estimate how long it will take to fill the tub to your desired level. In our case, we've calculated the fountain's "water speed," and now we're ready to use it to solve the main problem. But before we move on, let's make sure we really understand what this flow rate means. It's the key to unlocking the rest of the problem. So, remember, 1.25 liters per second is the magic number we'll be using next. Are you ready to see how we use it to find the time it takes to fill the 50-liter jug? Let's jump in!

Determining the Time to Fill 50 Liters

Alright, now that we know the flow rate is 1.25 liters per second, we can figure out how long it takes to fill a 50-liter jug. This is where things get really interesting! To do this, we'll use a slightly rearranged version of our flow rate formula. Remember, we had: Flow Rate = Volume / Time. This time, we want to find the Time, so we need to rearrange the formula. We can do this by multiplying both sides by Time and then dividing both sides by Flow Rate. This gives us: Time = Volume / Flow Rate. See? Simple algebra! Now, let's plug in the values we know. We want to find the time to fill a 50-liter jug, so Volume = 50 liters. And we know the flow rate is 1.25 liters per second. So, our equation becomes: Time = 50 liters / 1.25 liters per second. Let's do the division. 50 divided by 1.25 is 40. So, Time = 40 seconds. This means it will take 40 seconds to fill the 50-liter jug from the fountain. How cool is that? We used our understanding of flow rate and a little bit of math to solve the problem. Think about it this way: we knew how much water the fountain dispensed each second, and we knew how much water we needed to fill the jug. So, we just divided the total amount of water needed by the amount dispensed per second to find the total time. This is a great example of how physics and math can help us solve everyday problems. Now, let's recap what we've done and make sure we've got a solid understanding of the solution.

Recapping the Solution

Okay, let's take a step back and recap what we've accomplished. We started with a question: how long does it take to fill a 50-liter jug from a fountain that fills a 30-liter jug in 24 seconds? We broke this down into smaller steps to make it easier to solve. First, we calculated the flow rate of the fountain. We did this by dividing the volume of the first jug (30 liters) by the time it took to fill it (24 seconds). This gave us a flow rate of 1.25 liters per second. This means the fountain dispenses 1.25 liters of water every second. Next, we used this flow rate to calculate the time it would take to fill the 50-liter jug. We used the formula: Time = Volume / Flow Rate. Plugging in our values, we got: Time = 50 liters / 1.25 liters per second. This gave us a final answer of 40 seconds. So, it takes 40 seconds to fill the 50-liter jug. That's it! We solved the problem. We used basic physics principles and some simple math to find the answer. The key takeaway here is understanding the concept of flow rate and how it relates to volume and time. Once you grasp that, problems like these become much easier to tackle. And remember, this isn't just about filling jugs with water. This kind of thinking can be applied to all sorts of situations, from calculating how long it takes to drain a pool to figuring out how much fuel you need for a trip. So, keep practicing and keep exploring the world of physics! You never know what kind of cool problems you'll be able to solve.

Real-World Applications

So, we've solved our jug-filling problem, but you might be wondering,