Time Calculation Problems And Solutions

Hey guys! Let's dive into some time calculation problems. We'll break down each problem step by step so it's super easy to follow. These types of calculations are essential in many real-life situations, from scheduling events to understanding travel times. So, let’s get started and make sure we nail these calculations!

a) 7 hours 45 minutes 18 seconds + 4 hours 19 minutes 48 seconds

When we're tackling time addition, it’s all about keeping things organized. We add the seconds together, then the minutes, and finally the hours. If the seconds or minutes add up to 60 or more, we need to carry over to the next unit. Think of it like carrying over in regular addition, but with a base of 60 instead of 10.

First, let's add the seconds: 18 seconds + 48 seconds = 66 seconds. Since we have more than 60 seconds, we can convert 60 seconds into 1 minute. So, 66 seconds becomes 1 minute and 6 seconds. Write down 6 seconds and carry over 1 minute.

Next up, let’s add the minutes, including the carry-over: 45 minutes + 19 minutes + 1 minute (carried over) = 65 minutes. Again, we have more than 60 minutes, so we convert 60 minutes into 1 hour. This leaves us with 5 minutes and a carry-over of 1 hour. Write down 5 minutes and carry over 1 hour.

Now, let’s add the hours, including the carry-over: 7 hours + 4 hours + 1 hour (carried over) = 12 hours. So, there's no need to carry over here.

Putting it all together, we have 12 hours, 5 minutes, and 6 seconds. So, 7 hours 45 minutes 18 seconds + 4 hours 19 minutes 48 seconds = 12 hours 5 minutes 6 seconds. Isn't that neat? Breaking it down step by step makes it so much clearer!

b) 6 hours 5 minutes 21 seconds - 4 hours 37 minutes 52 seconds

Time subtraction can be a little trickier, especially when we need to borrow from the next unit. But don't worry, we'll walk through it together! Just like with addition, we'll subtract seconds from seconds, minutes from minutes, and hours from hours. If we don’t have enough seconds or minutes to subtract, we'll need to borrow.

Let’s start with the seconds: 21 seconds - 52 seconds. Uh-oh, we can’t subtract 52 from 21 directly. So, we need to borrow 1 minute from the minutes column. Remember, 1 minute is equal to 60 seconds. So, we borrow 1 minute (60 seconds) and add it to our 21 seconds, giving us 81 seconds. Now we can subtract: 81 seconds - 52 seconds = 29 seconds.

Moving on to the minutes, we borrowed 1 minute, so we now have 4 minutes left in the minutes column. We need to subtract 37 minutes from 4 minutes, which we can't do directly. So, we borrow 1 hour from the hours column. One hour is 60 minutes, so we add 60 minutes to our 4 minutes, giving us 64 minutes. Now, 64 minutes - 37 minutes = 27 minutes.

Finally, let’s subtract the hours. We borrowed 1 hour, so we now have 5 hours. 5 hours - 4 hours = 1 hour.

So, putting it all together, 6 hours 5 minutes 21 seconds - 4 hours 37 minutes 52 seconds = 1 hour 27 minutes 29 seconds. See, borrowing isn't so scary when we take it one step at a time!

c) (2 days 15 hours + 4 days 17 hours) / 4

This problem involves both addition and division, so let's break it down. First, we’ll add the times together, and then we’ll divide the result. Remember, there are 24 hours in a day, so we'll need to keep that in mind if we end up with more than 24 hours.

Let's add the days and hours: 2 days 15 hours + 4 days 17 hours. We add the days: 2 days + 4 days = 6 days. Then we add the hours: 15 hours + 17 hours = 32 hours. Now, 32 hours is more than a day, so let’s convert it. 32 hours is 1 day (24 hours) and 8 hours (32 - 24 = 8).

So, we add the 1 day to our 6 days, giving us 7 days, and we have 8 hours left over. The total is 7 days and 8 hours.

Now we need to divide 7 days 8 hours by 4. Let's start by converting everything to hours. 7 days is 7 * 24 = 168 hours. So, we have 168 hours + 8 hours = 176 hours.

Now, we divide 176 hours by 4: 176 hours / 4 = 44 hours. To make this more readable, let’s convert it back to days and hours. 44 hours is 1 day (24 hours) and 20 hours (44 - 24 = 20).

Therefore, (2 days 15 hours + 4 days 17 hours) / 4 = 1 day 20 hours. Awesome job on tackling this one!

d) (9 days 2 hours - 5 days 4 hours) * 3

For this problem, we’re dealing with subtraction and multiplication. Just like before, we’ll handle the subtraction first, and then multiply the result. Let’s get to it!

First, let's subtract the times: 9 days 2 hours - 5 days 4 hours. We subtract the days: 9 days - 5 days = 4 days. Now, we need to subtract the hours: 2 hours - 4 hours. We can't subtract 4 from 2, so we need to borrow 1 day from the days column. Remember, 1 day is 24 hours. So, we borrow 1 day (24 hours) and add it to our 2 hours, giving us 26 hours.

Now we can subtract: 26 hours - 4 hours = 22 hours. We borrowed 1 day, so we have 3 days left in the days column. So, the result of the subtraction is 3 days 22 hours.

Next, we need to multiply 3 days 22 hours by 3. Let’s convert everything to hours first. 3 days is 3 * 24 = 72 hours. So, we have 72 hours + 22 hours = 94 hours.

Now, we multiply 94 hours by 3: 94 hours * 3 = 282 hours. Let’s convert this back to days and hours. 282 hours / 24 hours per day = 11 days with a remainder of 18 hours (282 - 11 * 24 = 18).

So, (9 days 2 hours - 5 days 4 hours) * 3 = 11 days 18 hours. You're doing great! We've tackled some complex time calculations here.

Conclusion

Time calculations might seem a bit tricky at first, but with a little practice, they become second nature. We've covered addition, subtraction, division, and multiplication of time units, and you’ve seen how to borrow and carry over when needed. Keep practicing, and you’ll be a time calculation pro in no time! Remember, the key is to break down the problems into smaller steps and stay organized. You got this!