Hey guys! Let's break down this calculation together. It seems like we're trying to figure out a total time, expressed in hours, minutes, and seconds. The core idea here is to convert everything into a single unit, do the addition, and then convert back to the familiar hours, minutes, and seconds format. This is a common task in programming, data analysis, and even just everyday life when you're trying to manage your schedule or calculate elapsed time. So, stick with me, and we'll get through it step by step!

Breaking Down the Time Components

First, let's identify what we are working with:

• We have 3 hours.
• We have 15 minutes.
• We have 1080 seconds.

The key to solving this problem is unit conversion. We need to convert all the time components into a single unit. Seconds are often the easiest choice for the initial conversion, then converting back to hours and minutes if necessary. So, let's get started!

Converting Hours to Seconds

We need to convert the 3 hours into seconds. We know that:

• 1 hour = 60 minutes
• 1 minute = 60 seconds

Therefore,

• 1 hour = 60 minutes * 60 seconds/minute = 3600 seconds

So, 3 hours is:

• 3 hours * 3600 seconds/hour = 10800 seconds

This conversion is crucial because it allows us to add the hours to the other time units, which are already in minutes and seconds. Understanding this conversion factor is essential for accurate time calculations. Think of it as translating different languages; you need a common language (in this case, seconds) to understand the total meaning.

Converting Minutes to Seconds

Next, we need to convert the 15 minutes into seconds. We know that:

• 1 minute = 60 seconds

Therefore,

• 15 minutes * 60 seconds/minute = 900 seconds

Now we have all our time components in seconds, ready for addition. It's important to double-check these conversions to avoid errors in the final result. Many time-related problems involve multiple conversions, so practice makes perfect!

Summing Up the Seconds

Now that everything is in seconds, we can add up all the values:

• Total seconds = (3 hours in seconds) + (15 minutes in seconds) + (1080 seconds)
• Total seconds = 10800 seconds + 900 seconds + 1080 seconds
• Total seconds = 12780 seconds

So, the total time is 12780 seconds. But that's not super intuitive for most people! We usually want to express time in hours, minutes, and seconds. Let's do those conversions now.

Converting Back to Hours, Minutes, and Seconds

Okay, we have the total time in seconds (12780 seconds). Now we need to convert this back into hours, minutes, and seconds to make it more readable. The process involves dividing by the appropriate conversion factors and finding the remainders.

Converting Seconds to Hours

First, let's find out how many whole hours are in 12780 seconds:

• Hours = Total seconds / 3600 seconds/hour
• Hours = 12780 seconds / 3600 seconds/hour = 3.55 hours

So, we have 3 full hours. Now, let's find the remaining seconds after accounting for the full hours:

• Remaining seconds = Total seconds - (3 hours * 3600 seconds/hour)
• Remaining seconds = 12780 seconds - (3 * 3600) seconds
• Remaining seconds = 12780 seconds - 10800 seconds
• Remaining seconds = 1980 seconds

So, after taking out the full hours, we have 1980 seconds left. This will be used to calculate the minutes and remaining seconds.

Converting Remaining Seconds to Minutes

Now, let's convert the remaining 1980 seconds into minutes:

• Minutes = Remaining seconds / 60 seconds/minute
• Minutes = 1980 seconds / 60 seconds/minute = 33 minutes

So, we have 33 full minutes. Now, let's find the remaining seconds after accounting for the full minutes:

• Remaining seconds = Remaining seconds - (33 minutes * 60 seconds/minute)
• Remaining seconds = 1980 seconds - (33 * 60) seconds
• Remaining seconds = 1980 seconds - 1980 seconds
• Remaining seconds = 0 seconds

Great! We have no seconds remaining. This means that the 1980 seconds convert perfectly into 33 minutes.

Final Result

Putting it all together:

• 3 hours
• 33 minutes
• 0 seconds

Therefore, 3 hours + 15 minutes + 1080 seconds = 3 hours, 33 minutes, and 0 seconds.

Summary and Key Takeaways

In summary, we took three different time measurements (3 hours, 15 minutes, and 1080 seconds), converted them all to seconds, added them up, and then converted the total back into hours, minutes, and seconds. This process involved understanding the conversion factors between hours, minutes, and seconds.

Key Takeaways:

1. Unit Conversion: Always ensure that all values are in the same unit before performing arithmetic operations. For time calculations, converting everything to seconds is often the easiest approach.
2. Conversion Factors: Remember the conversion factors: 1 hour = 60 minutes = 3600 seconds and 1 minute = 60 seconds.
3. Step-by-Step Approach: Break the problem down into smaller, manageable steps. Convert hours to seconds, then minutes to seconds, add them up, and finally, convert back to hours, minutes, and seconds.
4. Double-Check: Always double-check your calculations, especially when dealing with multiple conversions. A small error early on can propagate through the entire calculation.
5. Practice: The more you practice these types of conversions, the easier they will become. Try different examples and challenge yourself to solve them quickly and accurately.

By following these steps, you can confidently solve similar time calculation problems. Understanding the underlying principles will help you apply this knowledge to various real-world scenarios.