A man travelled a certain distance by train at the rate of 25 kmph, and walked back at the rate of 4kmph. If the whole journey took 5 hours 48 minutes, the distance was

Options

A. a) 25km
B. b) 30km
C. c) 20km
D. d) 15km

Answer

To solve the problem, we need to find the distance traveled by the man. Let's break it down step by step.

### Step 1: Convert the total time into hours
The total time taken for the journey is given as 5 hours and 48 minutes. We need to convert this into hours.

- **Calculation**:
\[ 5 \text{ hours} + \frac{48 \text{ minutes}}{60} = 5 + 0.8 = 5.8 \text{ hours} \]

### Step 2: Set up the distance and time equations
Let the distance one way (from A to B) be \( x \) km. The man travels this distance by train at a speed of 25 km/h and walks back at a speed of 4 km/h.

- **Time taken by train**:
\[ T_1 = \frac{x}{25} \]

- **Time taken by walking**:
\[ T_2 = \frac{x}{4} \]

### Step 3: Write the total time equation
The total time for the journey is the sum of the time taken by train and the time taken by walking. According to the problem, this total time is 5.8 hours.

- **Equation**:
\[ T_1 + T_2 = 5.8 \]
Substituting the expressions for \( T_1 \) and \( T_2 \):
\[ \frac{x}{25} + \frac{x}{4} = 5.8 \]

### Step 4: Find a common denominator and solve for \( x \)
The common denominator for 25 and 4 is 100. We can rewrite the equation:

- **Rewriting the equation**:
\[ \frac{4x}{100} + \frac{25x}{100} = 5.8 \]
Combining the fractions:
\[ \frac{29x}{100} = 5.8 \]

### Step 5: Solve for \( x \)
To isolate \( x \), multiply both sides by 100:
\[ 29x = 580 \]
Now divide by 29:
\[ x = \frac{580}{29} = 20 \text{ km} \]

### Conclusion
The distance one way (from A to B) is 20 km.