To find the sum of the times given, let's break down the process step by step:
1. Convert each time to minutes:
- [tex]\( 1 \text{ hour } 20 \text{ minutes} \)[/tex]
- [tex]\( 1 \text{ hour } = 1 \times 60 = 60 \text{ minutes} \)[/tex]
- Total: [tex]\( 60 + 20 = 80 \text{ minutes} \)[/tex]
- [tex]\( 2 \text{ hours } 40 \text{ minutes} \)[/tex]
- [tex]\( 2 \text{ hours } = 2 \times 60 = 120 \text{ minutes} \)[/tex]
- Total: [tex]\( 120 + 40 = 160 \text{ minutes} \)[/tex]
- [tex]\( 3 \text{ hours } 5 \text{ minutes} \)[/tex]
- [tex]\( 3 \text{ hours } = 3 \times 60 = 180 \text{ minutes} \)[/tex]
- Total: [tex]\( 180 + 5 = 185 \text{ minutes} \)[/tex]
2. Sum all the minutes:
- Adding the minutes together: [tex]\( 80 + 160 + 185 = 425 \text{ minutes} \)[/tex]
3. Convert total minutes back to hours and minutes:
- Total hours: [tex]\( \left\lfloor \frac{425}{60} \right\rfloor = 7 \text{ hours} \)[/tex]
- Remaining minutes: [tex]\( 425 \mod 60 = 5 \text{ minutes} \)[/tex]
The sum of the times [tex]\( 1 \text{ hour } 20 \text{ minutes}, 2 \text{ hours } 40 \text{ minutes}, \)[/tex] and [tex]\( 3 \text{ hours } 5 \text{ minutes} \)[/tex] is:
[tex]\[ 7 \text{ hours } 5 \text{ minutes} \][/tex]
Therefore, the correct answer is [tex]\( 7 \text{ hours } 5 \text{ minutes} \)[/tex].
