Sure, let's break down the problem and find out how many hours there are in each given time duration step-by-step.
(a) Hours in 2 weeks
1. First, recall that there are 7 days in a week.
2. There are 24 hours in a day.
3. Therefore, the number of hours in one week is [tex]\( 7 \times 24 = 168 \)[/tex] hours.
4. Finally, for 2 weeks, we multiply the number of hours in one week by 2:
[tex]\[
2 \times 168 = 336 \text{ hours}
\][/tex]
(b) Hours in 4 days
1. There are 24 hours in a day.
2. Therefore, for 4 days:
[tex]\[
4 \times 24 = 96 \text{ hours}
\][/tex]
(c) Hours in [tex]\(1 \frac{5}{6}\)[/tex] weeks
1. Convert the mixed fraction [tex]\(1 \frac{5}{6}\)[/tex] weeks to an improper fraction or a decimal:
[tex]\[
1 + \frac{5}{6} = \frac{6}{6} + \frac{5}{6} = \frac{11}{6} \text{ weeks} \quad \text{or} \quad 1.8333 \text{ weeks}
\][/tex]
2. We know that one week has 168 hours.
3. Therefore, for [tex]\(1 \frac{5}{6}\)[/tex] weeks or approximately 1.8333 weeks:
[tex]\[
1.8333 \times 168 = 308 \text{ hours}
\][/tex]
(d) Hours in 2 weeks and 1 day
1. First, calculate the hours in 2 weeks, which we found earlier as 336 hours.
2. Then, calculate the hours in 1 day:
[tex]\[
1 \times 24 = 24
\][/tex]
3. Add the hours from 2 weeks and 1 day:
[tex]\[
336 + 24 = 360 \text{ hours}
\][/tex]
(e) Hours in 8 days
1. There are 24 hours in a day.
2. Therefore, for 8 days:
[tex]\[
8 \times 24 = 192 \text{ hours}
\][/tex]
(f) Hours in [tex]\(10 \frac{1}{6}\)[/tex] days
1. Convert the mixed fraction [tex]\(10 \frac{1}{6}\)[/tex] days to an improper fraction or a decimal:
[tex]\[
10 + \frac{1}{6} = \frac{60}{6} + \frac{1}{6} = \frac{61}{6} \text{ days} \quad \text{or} \quad 10.1667 \text{ days}
\][/tex]
2. We know there are 24 hours in a day.
3. Therefore, for [tex]\(10 \frac{1}{6}\)[/tex] days or approximately 10.1667 days:
[tex]\[
10.1667 \times 24 = 244 \text{ hours}
\][/tex]
So, summarizing the results:
(a) 2 weeks: 336 hours \
(b) 4 days: 96 hours \
(c) [tex]\(1 \frac{5}{6}\)[/tex] weeks: 308 hours \
(d) 2 weeks and 1 day: 360 hours \
(e) 8 days: 192 hours \
(f) [tex]\(10 \frac{1}{6}\)[/tex] days: 244 hours
