Calculating Play Time Duration A Math Problem

Have you ever been so engrossed in a play that you lost track of time? It's a common experience, especially when the performance is captivating. But what if you needed to calculate the exact duration of a play? Let's dive into a time calculation problem that will help us figure out just that. We'll explore how to convert minutes into hours and minutes, a skill that's not only useful for theatergoers but also for anyone managing their time effectively.

Understanding the Problem: The Play's Duration

Alright, guys, let's break down this theatrical time challenge. Imagine you're settling into your seat at the theater, the lights dim, and the curtain rises promptly at 8:30 PM (20 h 30 min). The play unfolds, full of drama and intrigue, and you're completely absorbed. Now, the crucial question: if the play lasts for 105 minutes, what time will the final curtain fall? This is where our time conversion skills come into play. We need to figure out how to express 105 minutes in terms of hours and minutes to determine the play's ending time. This problem is a fantastic example of how mathematical concepts can be applied to everyday situations, making math not just a subject in school, but a practical tool for navigating our daily lives. So, let's put on our thinking caps and get ready to solve this time calculation puzzle!

Converting Minutes to Hours and Minutes

Okay, so the first thing we need to tackle is converting those 105 minutes into a more manageable format. We all know that there are 60 minutes in an hour, right? So, our mission here is to figure out how many full hours are packed into those 105 minutes, and what's left over. Think of it like dividing a pizza: each "slice" is 60 minutes, and we want to see how many whole slices we can get. To do this, we perform a simple division: 105 minutes divided by 60 minutes per hour. When you do the math, you'll find that 105 divided by 60 equals 1 with a remainder of 45. What does this mean, you ask? Well, it tells us that 105 minutes is equal to 1 full hour (that's the "1" we got from the division) and 45 minutes (that's the remainder). So, we've successfully converted 105 minutes into 1 hour and 45 minutes. This is a crucial step in solving our problem, as it allows us to add the duration of the play to its starting time in a clear and straightforward way. Now that we've got this conversion down, we're one step closer to figuring out when the play ends!

Calculating the End Time

Now that we know the play lasts for 1 hour and 45 minutes, we can figure out the final curtain call time. Remember, the play started at 8:30 PM (20 h 30 min). To find the end time, we simply need to add the duration of the play (1 hour and 45 minutes) to the starting time. Let's break this down. First, we add the hours: 20 hours + 1 hour = 21 hours. Then, we add the minutes: 30 minutes + 45 minutes = 75 minutes. But hold on! We can't have 75 minutes in our final time because there are only 60 minutes in an hour. So, what do we do? We need to convert those extra minutes into hours and minutes. Just like before, we know that 60 minutes makes an hour. So, within those 75 minutes, there's one full hour (60 minutes) and a remainder of 15 minutes (75 - 60 = 15). This means we add that extra hour to our previous total of 21 hours, giving us 22 hours. And we're left with 15 minutes. So, the play ends at 22 hours and 15 minutes, which is 10:15 PM. See how breaking the problem down into smaller steps made it much easier to solve? We first converted the total minutes into hours and minutes, and then we added that duration to the starting time, making sure to handle any extra minutes by converting them into hours. Great job, we're almost at the final act of our problem-solving journey!

Identifying the Correct Answer

Alright, folks, we've done the hard work of calculating the duration and end time of the play. Now comes the satisfying part: matching our solution to the given options. We figured out that the play lasted for 1 hour and 45 minutes, and it ended at 10:15 PM (22 h 15 min). So, let's take a look at those answer choices again:

(A) 1 h 5 min (B) 1 h 25 min (C) 1 h 30 min (D) 1 h 45 min

Which one matches our calculation of the play's duration? You guessed it – option (D), 1 hour and 45 minutes, is the correct answer! We've successfully navigated the time calculation, converted minutes into hours and minutes, and accurately determined the play's duration. This exercise demonstrates how understanding basic mathematical principles can help us solve real-world problems, even something as enjoyable as figuring out the timing of a theatrical performance. Give yourselves a pat on the back; you've earned it!

Conclusion: Time Mastery Achieved

Well, everyone, we've reached the final act of our time calculation drama, and what a performance it's been! We started with a seemingly simple question – how long did the play last? – but along the way, we've honed some crucial mathematical skills. We learned how to convert minutes into hours and minutes, a skill that's incredibly useful in many everyday situations, from planning your schedule to managing your time effectively. We also practiced adding time durations, a skill that can help you figure out arrival times, calculate travel durations, and much more. And, most importantly, we saw how math isn't just about numbers on a page; it's a powerful tool for understanding and navigating the world around us. So, the next time you're at a play, a movie, or any event with a set duration, you'll be well-equipped to calculate the ending time with confidence. Keep practicing, keep exploring, and keep applying your mathematical skills to the world around you. You've got this!