If a man covers 10 (1/5) km in 3 hours, the distance covered by him in 5 hours is:Options18 km16 km17 km15 km

1. Break Down the Problem

We need to calculate the distance a man can cover in 5 hours, given that he covers $10 \frac{1}{5}$ km in 3 hours.

2. Relevant Concepts

To find the speed of the man, we can use the formula: $\text{Speed} = \frac{\text{Distance}}{\text{Time}}$ After finding the speed, we can then calculate the distance covered in 5 hours using: $\text{Distance} = \text{Speed} \times \text{Time}$

3. Analysis and Detail

1. Convert the mixed number $10 \frac{1}{5}$ km to an improper fraction: $10 \frac{1}{5} = 10 + \frac{1}{5} = \frac{50}{5} + \frac{1}{5} = \frac{51}{5} \text{ km}$

2. Calculate the speed: $\text{Speed} = \frac{\frac{51}{5} \text{ km}}{3 \text{ hours}} = \frac{51}{15} \text{ km/h} = \frac{17}{5} \text{ km/h}$

3. Calculate the distance covered in 5 hours: $\text{Distance} = \text{Speed} \times \text{Time} = \frac{17}{5} \text{ km/h} \times 5 \text{ hours} = 17 \text{ km}$

4. Verify and Summarize

The calculations confirm that with the derived speed, the distance covered in 5 hours is indeed 17 km.

Final Answer

The distance covered by him in 5 hours is 17 km.