To determine the distance a man will cover walking at a speed of \(2 \frac{4}{5}\) kilometers per hour for \(2 \frac{1}{2}\) hours, follow these steps:
1. Convert the mixed numbers to improper fractions:
- For the speed:
[tex]\[
2 \frac{4}{5} = 2 + \frac{4}{5} = \frac{2 \times 5 + 4}{5} = \frac{10 + 4}{5} = \frac{14}{5} \text{ km/h}
\][/tex]
- For the time:
[tex]\[
2 \frac{1}{2} = 2 + \frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{4 + 1}{2} = \frac{5}{2} \text{ hours}
\][/tex]
2. Convert the fractions to decimals for easier multiplication:
- \(2 \frac{4}{5}\) becomes \(2.8\) km/h.
- \(2 \frac{1}{2}\) becomes \(2.5\) hours.
3. Multiply the speed by the time to find the total distance:
[tex]\[
\text{Distance} = \text{Speed} \times \text{Time}
\][/tex]
Substituting the values:
[tex]\[
\text{Distance} = 2.8 \, \text{km/h} \times 2.5 \, \text{hours}
\][/tex]
Simplifying this multiplication:
[tex]\[
\text{Distance} = 7.0 \, \text{km}
\][/tex]
Therefore, the man will cover a total distance of 7.0 kilometers in [tex]\(2 \frac{1}{2}\)[/tex] hours walking at a speed of [tex]\(2 \frac{4}{5}\)[/tex] kilometers per hour.
