Tank Filling Problem: Calculate Individual Tap Contributions

Hey guys! Ever wondered how to figure out how much each tap contributes when filling a tank with multiple taps running at different rates? This is a classic math problem, and we're going to break it down step by step. So, let's dive into this problem where we have a 12150-liter tank being filled by three taps, each with its own flow rate. We'll figure out how much each tap contributes to filling the tank, rounding our answers to the nearest ten liters. Let's get started!

Understanding the Problem

So, here's the deal: we have a tank with a total capacity of 12150 liters. Imagine it like a big water container you might use for a pool or a large aquarium. Now, we're not filling this tank with just one tap, but three! Each of these taps flows at a different rate, kind of like having different sized hoses filling up a pool.

• The first tap is flowing at a rate of 14.6 liters per second (l/s). That's our speedy tap!
• The second tap flows at 8.9 l/s – a bit slower, but still contributing a good amount.
• The third tap is the slowest of the bunch, flowing at 4.2 l/s.

Our mission, should we choose to accept it (and we do!), is to figure out how much water each of these taps contributes to filling up the entire 12150-liter tank. We need to find out the individual contribution of each tap. But there's a twist! We need to provide our answer by approximating to the nearest ten liters. This means we'll round our final answers to the closest multiple of ten. So, if a tap fills 3478 liters, we'll round it to 3480 liters. Got it? Awesome! Let's move on to figuring out how to solve this.

Step 1: Calculate the Total Flow Rate

Okay, so the very first thing we need to figure out is the total flow rate of all three taps combined. Think of it like this: if you have three hoses filling a pool, you need to know how much water is coming in from all the hoses together to figure out how long it will take to fill the pool. In our case, we need to know the combined flow rate to determine how long the taps are running and, ultimately, how much each tap contributes.

To get the total flow rate, it's super simple: we just add up the individual flow rates of each tap. So, we're adding the 14.6 l/s from the first tap, the 8.9 l/s from the second tap, and the 4.2 l/s from the third tap. Let's do the math:

14. 6 l/s + 8.9 l/s + 4.2 l/s = 27.7 l/s

So, the total flow rate is 27.7 liters per second. This means that every second, 27.7 liters of water are flowing into the tank from all three taps combined. This is a crucial number because it tells us how quickly the tank is filling up overall. Now that we know the total flow rate, we can move on to the next step: figuring out how long it takes to fill the entire tank.

Step 2: Determine the Total Filling Time

Now that we know the total flow rate, which we calculated as 27.7 liters per second, we need to figure out how long it takes for all three taps working together to fill the entire tank. This is like figuring out how long it will take to fill that pool if you know how many gallons per minute are coming from all your hoses.

We know the tank's total capacity is 12150 liters. So, we have the total volume we need to fill and the rate at which we're filling it. To find the time, we're going to use a simple formula:

Time = Total Volume / Flow Rate

In our case:

Time = 12150 liters / 27.7 l/s

Let's do that division:

Time ≈ 438.63 seconds

So, it takes approximately 438.63 seconds to fill the tank completely. That's about 7 minutes and 18 seconds (since there are 60 seconds in a minute). Now, we have the total time the taps are running. This is super important because it's the key to figuring out how much each tap contributes individually. We know how fast each tap flows, and we know how long they flow for. Next up, we'll put those pieces together!

Step 3: Calculate Individual Contributions

Alright, we've reached the moment of truth! We know the flow rate of each tap, and we know the total time they're running to fill the tank (approximately 438.63 seconds). Now, we can finally calculate how much each tap contributed individually to the total 12150 liters. Think of it like figuring out how many slices of pizza each person ate if you know how fast they eat and how long everyone was eating.

The formula we'll use here is pretty straightforward:

Volume contributed by a tap = Tap's flow rate × Total filling time

We're going to do this calculation for each of the three taps:

• Tap 1: Flow rate = 14.6 l/s Volume contributed = 14.6 l/s × 438.63 s ≈ 6404.0 liters
• Tap 2: Flow rate = 8.9 l/s Volume contributed = 8.9 l/s × 438.63 s ≈ 3903.8 liters
• Tap 3: Flow rate = 4.2 l/s Volume contributed = 4.2 l/s × 438.63 s ≈ 1842.2 liters

So, we've got the approximate contributions from each tap. But remember, there's a slight twist! We need to provide our answers rounded to the nearest ten liters. Let's do that rounding in the next step.

Step 4: Round to the Nearest Ten Liters

We're almost there, guys! We've calculated the individual contributions of each tap, but remember the problem asked us to round our answers to the nearest ten liters. This is a common practice in real-world situations where exact precision might not be necessary, and a good estimate is perfectly fine. Think of it like estimating how many gallons of gas you need for a trip – you don't need the exact milliliter, just a good ballpark figure.

Let's take the volumes we calculated in the last step and round them:

• Tap 1: 6404.0 liters rounds to 6400 liters
• Tap 2: 3903.8 liters rounds to 3900 liters
• Tap 3: 1842.2 liters rounds to 1840 liters

So, now we have our final answers, rounded to the nearest ten liters. This gives us a good, clean estimate of how much each tap contributed to filling the 12150-liter tank. Let's recap our results and make sure everything makes sense!

Final Answer

Okay, let's bring it all together! We've gone through the steps, done the calculations, and rounded our answers. We started with a 12150-liter tank being filled by three taps with different flow rates. Our mission was to figure out how much each tap contributed, rounded to the nearest ten liters.

Here's what we found:

• Tap 1 (14.6 l/s): Contributed approximately 6400 liters
• Tap 2 (8.9 l/s): Contributed approximately 3900 liters
• Tap 3 (4.2 l/s): Contributed approximately 1840 liters

To make sure we're on the right track, let's do a quick check. If we add up the rounded contributions from each tap:

6400 liters + 3900 liters + 1840 liters = 12140 liters

This is very close to the total tank capacity of 12150 liters! The slight difference is due to the rounding we did along the way, but overall, our answers make sense. The tap with the highest flow rate (Tap 1) contributed the most, and the tap with the lowest flow rate (Tap 3) contributed the least. This is exactly what we'd expect.

So there you have it! We've successfully solved the tank-filling problem. You now know how to break down a problem involving multiple flow rates and calculate individual contributions. This kind of problem-solving skill is super useful in many real-world situations, from managing resources to understanding processes. Great job, everyone!