Sure! Let's break down the problem step-by-step.
### Step 1: Convert the Time to Minutes
First, we'll convert the given time into total minutes.
- 1 day = 24 hours = 24 * 60 minutes = 1440 minutes
- 1 hour = 60 minutes
Given time:
- Days: 18
- Hours: 20
- Minutes: 40
Calculate the total minutes:
- Minutes from days: [tex]\( 18 \text{ days} \times 1440 \text{ minutes/day} = 25920 \text{ minutes} \)[/tex]
- Minutes from hours: [tex]\( 20 \text{ hours} \times 60 \text{ minutes/hour} = 1200 \text{ minutes} \)[/tex]
- Minutes from the given minutes: [tex]\( 40 \text{ minutes} \)[/tex]
Add them up:
- [tex]\( 25920 \text{ minutes} + 1200 \text{ minutes} + 40 \text{ minutes} = 27160 \text{ minutes} \)[/tex]
So, the total time in minutes is 27160 minutes.
### Step 2: Perform the Division
Now, we need to divide the total minutes by the divisor (5).
Calculate:
[tex]\[ \frac{27160 \text{ minutes}}{5} = 5432 \text{ minutes} \][/tex]
### Step 3: Convert the Result Back to Days, Hours, and Minutes
Next, we'll convert the quotient back into days, hours, and minutes.
- 1 day = 1440 minutes
- 1 hour = 60 minutes
Calculate:
1. Number of days:
[tex]\[ \text{Days} = \left\lfloor \frac{5432 \text{ minutes}}{1440 \text{ minutes/day}} \right\rfloor = 3 \text{ days} \][/tex]
2. Remaining minutes after extracting days:
[tex]\[ 5432 \text{ minutes} \mod 1440 \text{ minutes/day} = 1112 \text{ minutes} \][/tex]
3. Number of hours from the remaining minutes:
[tex]\[ \text{Hours} = \left\lfloor \frac{1112 \text{ minutes}}{60 \text{ minutes/hour}} \right\rfloor = 18 \text{ hours} \][/tex]
4. Remaining minutes after extracting hours:
[tex]\[ 1112 \text{ minutes} \mod 60 \text{ minutes/hour} = 32 \text{ minutes} \][/tex]
So, the final result after dividing and converting back is:
- 3 days
- 18 hours
- 32 minutes
### Summary
The original time of 18 days, 20 hours, and 40 minutes when divided by 5 results in:
[tex]\[ 3 \text{ days}, 18 \text{ hours}, \text{ and } 32 \text{ minutes} (with a total of 5432 minutes). \][/tex]
