Solving The Leaky Tank Problem Step-by-Step

Hey guys! Ever stumbled upon a math problem that seems like a real head-scratcher? Well, today we're diving deep into a classic: the leaky water tank conundrum. Imagine you've got a tank brimming with water, and then, whoosh, some gets taken out, and then even more! The big question is, how much water is left? Let's break down this problem step by step, making it super easy to understand. So, grab your thinking caps, and let's get started!

The Leaky Tank Problem: A Deep Dive

Our leaky tank problem begins with a tank that's absolutely full, holding a whopping 120 liters of water. Now, the twist comes when we start removing water in stages. First, a hefty 5/8 of the tank's contents is drawn out. That's a significant chunk, right? But wait, there's more! After this initial withdrawal, we then take out 1/6 of the water that remains. This is where it gets interesting because we're not taking 1/6 of the original amount, but 1/6 of what's left after the first removal. To solve this, we need to carefully calculate each step, understanding how the water level changes each time. Our ultimate goal? To figure out exactly how many liters are still sloshing around in the tank at the end of this watery saga. So, let's put on our math hats and get to work, unraveling this problem one step at a time!

Step 1: Calculating the Initial Water Removal

Okay, so the first thing we need to figure out is how much water was taken out in that initial 5/8 removal. We know the tank started with 120 liters, so we need to find 5/8 of that amount. Remember, in math, "of" often means multiply. So, we're going to multiply 5/8 by 120 liters. Here's how it looks:

(5/8) * 120 liters = ?

To solve this, you can either multiply 5 by 120 first and then divide by 8, or you can simplify things by dividing 120 by 8 first. Let's do that! 120 divided by 8 is 15. Now we have:

5 * 15 liters = ?

Multiply that out, and you get 75 liters. So, that's a big gulp of water gone – 75 liters were removed in the first step. But we're not done yet! We need to know how much water is left in the tank after this initial removal. This is crucial for the next step, so let's figure it out. We started with 120 liters, took out 75, so a little subtraction will tell us the tale.

Step 2: Determining the Remaining Water After the First Removal

Alright, we know we started with 120 liters in our trusty tank, and after the first big draw, a hefty 75 liters were taken out. So, to figure out how much water is still sloshing around, we need to do a little subtraction. We're going to take the initial amount and subtract the amount removed:

120 liters - 75 liters = ?

This is a pretty straightforward subtraction problem. When you do the math, you'll find that 120 minus 75 equals 45. So, after the first removal, we have 45 liters of water left in the tank. This is a key number because it's the starting point for our next calculation. Remember, the problem tells us that another amount of water is removed, but this time it's a fraction of the remaining water, not the original amount. So, we're not dealing with the initial 120 liters anymore; we're working with these 45 liters. This is a crucial distinction to grasp to get the right answer. Now that we know how much water is left, we can move on to the next step: figuring out how much water is removed in that second withdrawal.

Step 3: Calculating the Second Water Removal

Okay, things are getting interesting! We've already navigated the first big water removal, and we know that 45 liters are currently residing in our tank. Now, the problem throws another curveball: 1/6 of the remaining water is taken out. This is where it's super important to pay attention to the details. We're not taking 1/6 of the original 120 liters; we're dealing with 1/6 of the 45 liters that are left. So, how do we figure this out? Just like before, when we see "of" in a math problem, it usually means we need to multiply. In this case, we're going to multiply 1/6 by 45 liters. Here's the equation:

(1/6) * 45 liters = ?

To solve this, you can either multiply 1 by 45 and then divide by 6, or you can think about dividing 45 by 6 directly. 45 divided by 6 is 7.5. So, that means 7.5 liters were removed in the second step. We're getting closer to the finish line! We know how much was removed in the second step, and we know how much was in the tank before that removal. Now, the final piece of the puzzle is to figure out how much water is finally left in the tank.

Step 4: Determining the Final Amount of Water Remaining

We're in the home stretch now, guys! We've done the hard work of figuring out the initial water removal, calculating the water left after that, and then determining the amount removed in the second step. We know that before the second removal, there were 45 liters in the tank, and we just figured out that 7.5 liters were taken out in that second step. So, to find the final amount of water remaining, we need to do one last subtraction. We're going to subtract the amount removed in the second step from the amount that was in the tank before that removal:

45 liters - 7.5 liters = ?

This subtraction might require a little careful lining up of the decimals, but it's nothing we can't handle! When you subtract 7.5 from 45, you get 37.5. So, that's it! After all the water withdrawals, there are 37.5 liters of water left in the tank. We've successfully navigated the leaky tank problem! Now, let's recap the whole journey and make sure we've got a solid understanding of how we got there.

Final Answer: 37.5 Liters

So, after all the calculations and step-by-step deductions, we've arrived at our final answer: there are 37.5 liters of water remaining in the tank. Woohoo! Give yourselves a pat on the back for sticking with it and conquering this problem. We started with a tank full of 120 liters, then took away 5/8 of it, followed by 1/6 of the remaining water, and through careful calculations, we've determined the final amount. Remember, the key to tackling problems like this is to break them down into smaller, more manageable steps. By focusing on each step individually and understanding what's happening at each stage, even the trickiest problems become solvable. And that, my friends, is the power of problem-solving! So, the next time you encounter a math challenge, remember our leaky tank adventure and tackle it with confidence. You've got this!

Why This Problem Matters: Real-World Applications

You might be thinking, "Okay, that's great, we solved the water tank problem, but when am I ever going to use this in real life?" That's a fair question! While you might not encounter a leaky tank scenario every day, the underlying concepts and skills we used to solve this problem are incredibly valuable in a wide range of real-world situations. Let's think about it. We dealt with fractions, which are used all the time in cooking, measuring, and even understanding discounts at the store. We worked with percentages, which are crucial for understanding things like interest rates, sales tax, and statistical data. And most importantly, we practiced problem-solving skills: breaking down a complex problem into smaller steps, carefully analyzing each step, and using logic and reasoning to arrive at a solution. These skills are essential in almost every aspect of life, from managing your finances to planning a project at work to making informed decisions about your health. So, while the leaky tank might seem like an abstract scenario, the skills you honed while solving it are very real and very applicable to your everyday life. Keep practicing those problem-solving muscles, and you'll be amazed at what you can accomplish!

Practice Makes Perfect: Similar Problems to Try

Now that we've successfully tackled the leaky tank problem, you might be feeling like a math whiz! But like any skill, problem-solving gets even better with practice. So, if you're up for a challenge, here are a few similar problems you can try to further sharpen your skills:

1. The Shrinking Cake: Imagine you have a delicious cake. You eat 1/3 of it, and then your friend eats 1/4 of what's left. How much of the cake is remaining?
2. The Discount Dilemma: A store is having a sale! Everything is 20% off, and then an additional 10% is taken off the sale price. If an item originally costs $50, what is the final price?
3. The Growing Savings Account: You deposit $100 into a savings account that earns 5% interest per year. After one year, you deposit another $50. How much money is in the account after two years?

These problems might seem a little different, but they all involve similar concepts to the leaky tank problem: fractions, percentages, and multi-step calculations. The key is to break each problem down into smaller steps, just like we did with the tank. Read the problem carefully, identify the key information, and then work through each step methodically. Don't be afraid to draw diagrams or write out equations to help you visualize the problem. And most importantly, don't give up! The more you practice, the more confident and skilled you'll become at problem-solving. So, grab a pencil and paper, and get ready to put your math muscles to work!

Conclusion: The Power of Step-by-Step Problem Solving

Alright, guys, we've reached the end of our leaky tank adventure! We started with a seemingly complex problem, but by breaking it down into manageable steps, we were able to successfully navigate the calculations and arrive at the solution. We learned how to work with fractions, understand the importance of careful reading and attention to detail, and most importantly, how to approach a problem systematically. Remember, the key takeaway from this exercise isn't just the answer itself (37.5 liters), but the process we used to get there. The ability to break down a problem into smaller steps, analyze each step carefully, and use logic and reasoning to arrive at a solution is a skill that will serve you well in all areas of life. So, the next time you're faced with a challenge, remember the leaky tank, and remember the power of step-by-step problem-solving. You've got this!