Walking at three-seventh of his usual speed, a man covers certain distance in 12 hours more than the time he takes to cover the distance at his usual speed. The time taken by him to cover the distance with his usual speed is:

Options

A. 4.5 hours
B. 5.5 hours
C. 6 hours
D. 9 hours

Answer

To solve the problem, we need to establish a relationship between speed, time, and distance. Let's break it down step by step.

### Step 1: Define Variables
Let the usual speed of the man be \( S \) (in any unit, e.g., km/h). The time taken to cover the distance at his usual speed will be denoted as \( T \) (in hours).

### Step 2: Express Distance
Using the formula for distance:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
The distance covered at his usual speed is:
\[ D = S \times T \]

### Step 3: Determine the New Speed
When the man walks at three-sevenths of his usual speed, his new speed becomes:
\[ \text{New Speed} = \frac{3}{7}S \]

### Step 4: Calculate Time at New Speed
The time taken to cover the same distance \( D \) at the new speed is:
\[ \text{New Time} = \frac{D}{\text{New Speed}} = \frac{S \times T}{\frac{3}{7}S} = \frac{7T}{3} \]

### Step 5: Set Up the Equation
According to the problem, the time taken at the new speed is 12 hours more than the time taken at the usual speed:
\[ \frac{7T}{3} = T + 12 \]

### Step 6: Solve the Equation
To solve for \( T \), first eliminate the fraction by multiplying the entire equation by 3:
\[ 7T = 3T + 36 \]
Now, simplify the equation:
\[ 7T - 3T = 36 \]
\[ 4T = 36 \]
\[ T = \frac{36}{4} = 9 \]

### Step 7: Conclusion
The time taken by him to cover the distance with his usual speed is:
\[ \boxed{9 \text{ hours}} \]