If a person travels `10(1)/(5)` km in 3 hours, then the distance covered by him in 5 hours will be:

Options

A. 18 km
B. 17 km
C. 16 km
D. 15 km

Answer

To solve the problem, we need to find out how far a person can travel in 5 hours if they travel \(10 \frac{1}{5}\) km in 3 hours. Let's break it down step by step.

### Step 1: Convert the mixed fraction to an improper fraction
The distance traveled is given as \(10 \frac{1}{5}\) km. We can convert this mixed number into an improper fraction.

\[ 10 \frac{1}{5} = 10 + \frac{1}{5} = \frac{50}{5} + \frac{1}{5} = \frac{51}{5} \text{ km} \]

**Hint:** To convert a mixed number to an improper fraction, multiply the whole number by the denominator and add the numerator.

### Step 2: Calculate the distance traveled in 1 hour
Now, we need to find out how much distance is covered in 1 hour. Since the person travels \(\frac{51}{5}\) km in 3 hours, we can find the distance per hour by dividing the total distance by the total time.

\[ \text{Distance in 1 hour} = \frac{\frac{51}{5} \text{ km}}{3 \text{ hours}} = \frac{51}{5} \times \frac{1}{3} = \frac{51}{15} \text{ km} \]

**Hint:** To find the distance per hour, divide the total distance by the total time.

### Step 3: Calculate the distance traveled in 5 hours
Next, we need to find out how far the person travels in 5 hours. We can do this by multiplying the distance traveled in 1 hour by 5.

\[ \text{Distance in 5 hours} = \frac{51}{15} \times 5 = \frac{51 \times 5}{15} = \frac{255}{15} = 17 \text{ km} \]

**Hint:** To find the total distance for a different time period, multiply the distance per hour by the number of hours.

### Conclusion
The distance covered by the person in 5 hours is **17 km**.

**Final Answer:** 17 km (Option B)

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