Calculating Plane Departure Time From London To Newcastle Airport

by BRAINLY IN FTUNILA 66 views
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Introduction

Hey guys! Let's dive into a cool math problem involving a plane journey. We've got a plane that flew from London City Airport to Newcastle Airport, covering a distance of 256 miles. It cruised at an average speed of 192 miles per hour and touched down at 19:15 (that's 7:15 PM in regular time). The big question is: What time did this plane take off from London City Airport? We're going to figure this out step-by-step, and by the end, you'll be a pro at solving similar time-related problems.

Understanding the Problem

Okay, so to get started, let’s break down what we know. We've got the distance (256 miles), the average speed (192 mph), and the arrival time (19:15). What we need to find is the departure time. The key here is to figure out how long the flight took. Once we know the flight duration, we can simply subtract that from the arrival time to find out when the plane left London City Airport. This is a classic example of a problem where understanding the relationship between distance, speed, and time is crucial. Remember the formula: Distance = Speed × Time? We're going to use that, but we'll need to rearrange it to solve for time. So, Time = Distance / Speed. This formula is our bread and butter for this problem. It’s super important to remember this, as it’s used in countless scenarios, not just math problems but also in real-life situations like planning a road trip or estimating travel time. Make sure you've got this formula down pat, guys! We'll be using it a lot, not just in this problem but in many others too.

Step 1 Calculating Flight Duration

Alright, let's get our hands dirty with some calculations. We know the distance is 256 miles and the speed is 192 mph. Using our formula, Time = Distance / Speed, we can plug in these values. So, Time = 256 miles / 192 mph. When you do the division, you get 1.3333... hours. Now, this isn’t super helpful as it is. We need to convert that decimal into minutes so we can work with it more easily. The '1' in 1.3333 hours represents one full hour, which is straightforward. But what about the '.3333'? This is where we need to do a little conversion. To convert the decimal part of an hour into minutes, we multiply it by 60 (since there are 60 minutes in an hour). So, 0.3333 hours * 60 minutes/hour gives us approximately 20 minutes. Therefore, the flight duration is 1 hour and 20 minutes. Knowing the exact flight duration is super important because it's the bridge that connects the arrival time to the departure time. Without this, we're just shooting in the dark. So, make sure you understand how we calculated this. It’s a fundamental step in solving this problem, and getting it right is crucial for finding the correct departure time. The good news is, once we have this, the rest is pretty smooth sailing. Hang in there, guys; we’re making great progress!

Step 2 Subtracting Flight Duration from Arrival Time

Okay, we've nailed down the flight duration: 1 hour and 20 minutes. Now comes the exciting part – figuring out the departure time. We know the plane landed at 19:15, and it was in the air for 1 hour and 20 minutes. To find the departure time, we need to subtract this flight duration from the arrival time. Think of it like rewinding time. We’re going back 1 hour and 20 minutes from 19:15. So, let’s do the subtraction. First, we subtract the minutes: 15 minutes – 20 minutes. Uh oh, we’ve got a problem! We can't subtract 20 minutes from 15 minutes directly. What do we do? Well, we need to borrow an hour from the 'hours' place. So, we borrow 1 hour (which is 60 minutes) from the 19 hours. This leaves us with 18 hours, and we add those 60 minutes to the original 15 minutes, giving us 75 minutes. Now we can subtract! 75 minutes – 20 minutes = 55 minutes. Next, we subtract the hours: 18 hours – 1 hour = 17 hours. So, the departure time is 17:55. This means the plane left London City Airport at 5:55 PM. See how we broke it down step by step? Subtracting time can be a bit tricky, but if you take it one step at a time – first the minutes, then the hours – you’ll get there. This skill is super handy, not just for math problems, but for everyday life too. So, great job on getting through this step, guys!

Final Answer and Conclusion

Woohoo! We've made it to the finish line. After carefully calculating the flight duration and subtracting it from the arrival time, we've determined that the plane left London City Airport at 17:55 (which is 5:55 PM). This wasn't just about finding a number; it was about understanding how time, distance, and speed relate to each other. We used the formula Time = Distance / Speed, converted decimals to minutes, and even did some borrowing when subtracting time. These are awesome skills to have in your math toolkit. Remember, guys, math isn't just about memorizing formulas; it's about applying them in real-world scenarios. Think about all the times you might use these skills in your life – planning a trip, figuring out how long it'll take to get somewhere, or even just managing your schedule. So, give yourselves a pat on the back for tackling this problem. You've shown that you can break down complex problems into smaller, manageable steps. And that’s a superpower, guys! Keep practicing, keep exploring, and keep having fun with math!

Summary of Key Steps

  1. Calculate the Flight Duration: Use the formula Time = Distance / Speed. In this case, Time = 256 miles / 192 mph = 1.3333 hours.
  2. Convert Decimal Hours to Minutes: Multiply the decimal part of the hours by 60. So, 0.3333 hours * 60 minutes/hour ≈ 20 minutes. Thus, the flight duration is 1 hour and 20 minutes.
  3. Subtract Flight Duration from Arrival Time: Subtract 1 hour and 20 minutes from the arrival time of 19:15. This gives us a departure time of 17:55.

Tips for Solving Similar Problems

  • Understand the Relationship: Always remember the relationship between distance, speed, and time (Distance = Speed × Time).
  • Convert Units: Make sure your units are consistent. If speed is in miles per hour, time should be in hours.
  • Break it Down: If the problem seems complex, break it down into smaller, manageable steps.
  • Practice Makes Perfect: The more you practice, the easier these problems will become. Try solving similar problems with different values to build your confidence.
  • Check Your Work: Always double-check your calculations to avoid errors. A small mistake can lead to a wrong answer.

Real-World Applications

The concepts we used in this problem are super useful in everyday life. Here are a few examples:

  • Planning a Trip: Estimating travel time when driving, flying, or taking public transportation.
  • Scheduling: Calculating how long tasks will take and planning your day effectively.
  • Sports: Determining the speed of a runner or a ball.
  • Navigation: Using GPS to estimate arrival times based on current speed and distance.

So, the next time you're faced with a time-related problem, remember the steps we used here. You've got this, guys!

Additional Practice Problems

Want to flex those math muscles even more? Here are a few extra problems you can try out:

  1. A car travels 300 miles at an average speed of 60 mph. If it arrives at 14:00, what time did it leave?
  2. A train journey is 450 miles long. If the train travels at an average speed of 90 mph and arrives at 21:30, what was its departure time?
  3. A cyclist rides 75 miles at an average speed of 15 mph. If they arrive at 16:45, what time did they start their ride?

Try solving these problems on your own, guys. Remember, practice is key to mastering these skills. And if you get stuck, just revisit the steps we covered in this article. You've got this!

Keep Learning!

Math is all around us, and the more you understand it, the better equipped you'll be to tackle real-world challenges. Keep exploring, keep asking questions, and most importantly, keep having fun with math. You're doing awesome, guys! Remember, every problem you solve is a step forward in your learning journey. So, keep challenging yourselves and keep growing. You've got the potential to do amazing things, and math is just one of the many tools you can use to achieve your goals. So, let's keep learning and keep making a difference. You guys are rockstars!