Let's solve the problem step by step to find out how long it would take Lau to walk to school at a speed of [tex]\(6 \text{ km/h}\)[/tex].
1. Convert the initial time to hours:
- Lau initially takes 5 minutes to walk to school.
- To convert minutes to hours, use the fact that 1 hour = 60 minutes.
[tex]\[
\text{Time in hours} = \frac{5 \text{ minutes}}{60} = 0.0833 \text{ (rounded to 4 decimal places)}
\][/tex]
2. Calculate the distance Lau walks:
- Lau's initial speed is [tex]\(16 \text{ km/h}\)[/tex].
- We use the formula for distance, [tex]\( \text{Distance} = \text{Speed} \times \text{Time} \)[/tex].
[tex]\[
\text{Distance} = 16 \text{ km/h} \times 0.0833 \text{ hours} = 1.3333 \text{ km} \text{ (rounded to 4 decimal places)}
\][/tex]
3. Calculate the new time it would take at the new speed:
- Lau's new speed is [tex]\(6 \text{ km/h}\)[/tex].
- To find the time, use the formula [tex]\( \text{Time} = \frac{\text{Distance}}{\text{Speed}} \)[/tex].
[tex]\[
\text{Time} = \frac{1.3333 \text{ km}}{6 \text{ km/h}} = 0.2222 \text{ hours} \text{ (rounded to 4 decimal places)}
\][/tex]
4. Convert the new time from hours to minutes:
- To convert hours to minutes, use the fact that 1 hour = 60 minutes.
[tex]\[
\text{Time in minutes} = 0.2222 \text{ hours} \times 60 = 13.3333 \text{ minutes} \text{ (rounded to 4 decimal places)}
\][/tex]
So, it would take Lau approximately 13.33 minutes to walk to school at a speed of [tex]\(6 \text{ km/h}\)[/tex].
