A movie starts at 3:10 PM and ends at 4:45 PM. How many minutes long is it

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Welcome to this lesson on calculating time durations. Today we'll learn how to find the length of a movie that starts at 3:10 PM and ends at 4:45 PM. Understanding time calculation is an essential life skill we use every day. Let's begin by reviewing how we read and understand time on a clock. Time is measured in hours and minutes, with each hour containing sixty minutes. Our goal is to find the difference between the start and end times to determine the movie's duration. Let's first understand how to read the given times: 3:10 PM and 4:45 PM. The first number represents hours, and the second number represents minutes past that hour. So 3:10 PM means 3 hours and 10 minutes in the afternoon. Similarly, 4:45 PM means 4 hours and 45 minutes in the afternoon. When calculating time differences, we need to work with both the hours and minutes components separately. Remember that each hour contains exactly sixty minutes, which is crucial for our calculations. Let's visualize this problem on a timeline to better understand what we're calculating. We'll draw a horizontal line representing time from 3:00 PM to 5:00 PM. We'll mark the start time at 3:10 PM and the end time at 4:45 PM. The distance between these two points represents the duration we need to find. This visual approach helps us see that we're measuring a span that crosses from one hour to another. Notice how the calculation involves both moving from 3:10 to 4:00 and then from 4:00 to 4:45. We'll solve this using two different methods to ensure we understand the concept thoroughly. Method one involves breaking the time into manageable segments. From 3:10 PM to 4:45 PM, we can split this into two parts: from 3:10 PM to 4:00 PM, and from 4:00 PM to 4:45 PM. This approach makes the calculation easier by dealing with round numbers. We'll calculate each segment separately and then add them together to get our final answer. Let's calculate the first segment: from 3:10 PM to 4:00 PM. Starting at 3:10 PM, we need to reach 4:00 PM, which means completing the current hour. Since each hour has sixty minutes, and we're already at 10 minutes past 3:00, we need 60 minus 10 equals 50 more minutes to reach 4:00 PM. So the first segment is exactly 50 minutes long. This calculation uses the fundamental principle that an hour contains sixty minutes. Now let's calculate the second segment: from 4:00 PM to 4:45 PM. This is straightforward since we're staying within the same hour. We simply take the minutes portion of the end time: 45 minutes. So the second segment is 45 minutes long. This part of the calculation is simple because we don't cross any hour boundaries. When both times are within the same hour, we can directly subtract the minute values. Now we add our two segments together to find the total movie duration. The first segment was 50 minutes, and the second segment was 45 minutes. Adding these together: 50 plus 45 equals 95 minutes. Therefore, the movie is 95 minutes long. This method works well when we can break the problem into logical segments. It's particularly useful when the time period crosses hour boundaries, as it helps us avoid calculation errors. Let's explore method two, which involves direct subtraction of the end time minus the start time. This method requires us to handle the hours and minutes together systematically. We'll subtract 3:10 from 4:45 directly, but we need to be careful with borrowing when necessary. This approach is more direct but requires understanding how to properly subtract time values. Both methods should give us the same answer, which helps verify our work. For direct subtraction, we write the problem as 4:45 minus 3:10. We align the hours under hours and minutes under minutes. This gives us 4 hours and 45 minutes minus 3 hours and 10 minutes. We can subtract the hours and minutes separately in this case since the minutes in the minuend are greater than the minutes in the subtrahend. When 45 minutes minus 10 minutes equals 35 minutes, and 4 hours minus 3 hours equals 1 hour. Continuing with our direct subtraction: 4 hours 45 minutes minus 3 hours 10 minutes equals 1 hour 35 minutes. However, our answer needs to be in minutes only, not in hours and minutes. To convert 1 hour 35 minutes to minutes only, we multiply the hours by 60 and add the remaining minutes. One hour equals 60 minutes, plus 35 minutes equals 95 minutes total. This confirms our previous answer using the segment method. What if we had a problem where the minutes in the start time were greater than the minutes in the end time? For example, if a movie started at 3:45 PM and ended at 4:10 PM, we'd need to borrow from the hour. We would convert one hour to sixty minutes, making it 3 hours 45 minutes becomes 2 hours 105 minutes. Then we could subtract normally: 105 minutes minus 45 minutes equals 60 minutes, and 3 hours minus 2 hours equals 1 hour. Understanding borrowing is crucial for more complex time calculations. There's another approach where we convert both times entirely to minutes past a reference point, such as noon or midnight. Starting with 3:10 PM, that's 3 hours and 10 minutes past noon, which equals 3 times 60 plus 10 equals 190 minutes past noon. The end time 4:45 PM equals 4 times 60 plus 45 equals 285 minutes past noon. Subtracting 285 minus 190 gives us 95 minutes. This method eliminates the complexity of handling hours and minutes separately. Let's verify our answer of 95 minutes makes sense. We can estimate: from 3:10 PM to 4:45 PM is roughly one and a half hours. One and a half hours equals 90 minutes, which is very close to our calculated 95 minutes. We can also check by adding 95 minutes to our start time: 3:10 PM plus 95 minutes. Ninety-five minutes equals 1 hour 35 minutes, so 3:10 PM plus 1 hour 35 minutes equals 4:45 PM, which matches our end time. This verification confirms our answer is correct. Common mistakes include forgetting that hours contain sixty minutes, not one hundred. Some students might calculate 4:45 minus 3:10 as 1:35 and think that's 135 minutes, which is incorrect. Others might forget to borrow when necessary in subtraction problems. Remember to always convert your final answer to the required units, and double-check your work using estimation or verification methods. Taking time to understand the underlying principles prevents these common errors. After using multiple methods and verifying our work, we can confidently state that the movie is 95 minutes long. We learned three different approaches: segmenting the time period, direct subtraction with proper handling of units, and converting everything to minutes. Each method has its advantages depending on the specific problem. The key principles are understanding that each hour contains sixty minutes, handling borrowing correctly, and always verifying your answer. These skills will help you solve any time duration problem you encounter.