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

Options

A. 25km
B. 30km
C. 20km
D. 15km

Answer

To solve the problem step by step, we will define the distance traveled by the man and calculate the time taken for both parts of the journey.

### Step 1: Define the distance
Let the distance traveled by the man be \( x \) kilometers.

### Step 2: Calculate the time taken for each part of the journey
- The time taken to travel by train at 25 km/h is given by the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{x}{25} \text{ hours} \]
- The time taken to walk back at 4 km/h is:
\[ \text{Time} = \frac{x}{4} \text{ hours} \]

### Step 3: Set up the equation for total time
The total time for the journey is given as 5 hours and 48 minutes. We need to convert 48 minutes into hours:
\[ 48 \text{ minutes} = \frac{48}{60} = 0.8 \text{ hours} \]
Thus, the total time is:
\[ 5 + 0.8 = 5.8 \text{ hours} \]

Now, we can set up the equation:
\[ \frac{x}{25} + \frac{x}{4} = 5.8 \]

### Step 4: Find a common denominator and simplify
The least common multiple (LCM) of 25 and 4 is 100. We will convert both fractions to have a common denominator:
\[ \frac{x}{25} = \frac{4x}{100} \quad \text{and} \quad \frac{x}{4} = \frac{25x}{100} \]
So, we can rewrite the equation as:
\[ \frac{4x}{100} + \frac{25x}{100} = 5.8 \]
Combining the fractions gives:
\[ \frac{29x}{100} = 5.8 \]

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

### Final Answer
The distance traveled by the man is \( 20 \) kilometers.

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