If a man reduces his speed to 2/3, he takes 1 hours more in walking a certain distance. The time (in hours) to cover the distance with his normal speed is

Options

A. 2
B. 1
C. 3
D. `1.5`

Answer

To solve the problem step by step, let's denote the following:

- Let the normal speed of the man be \( S \) (in km/h).
- Let the distance he needs to cover be \( D \) (in km).
- Let the time taken to cover the distance at normal speed be \( T \) (in hours).

### Step 1: Express the normal time in terms of speed and distance
Using the formula for time, we have:
\[ T = \frac{D}{S} \]

### Step 2: Express the reduced speed
When the man reduces his speed to \( \frac{2}{3} \) of his normal speed, his new speed becomes:
\[ \text{Reduced Speed} = \frac{2}{3}S \]

### Step 3: Express the time taken at reduced speed
The time taken to cover the same distance at the reduced speed is:
\[ T' = \frac{D}{\frac{2}{3}S} = \frac{3D}{2S} \]

### Step 4: Set up the equation based on the problem statement
According to the problem, the time taken at the reduced speed is 1 hour more than the time taken at normal speed:
\[ T' = T + 1 \]
Substituting the expressions for \( T \) and \( T' \):
\[ \frac{3D}{2S} = \frac{D}{S} + 1 \]

### Step 5: Clear the fractions
To eliminate the fractions, multiply the entire equation by \( 2S \):
\[ 3D = 2D + 2S \]

### Step 6: Simplify the equation
Rearranging gives:
\[ 3D - 2D = 2S \implies D = 2S \]

### Step 7: Substitute back to find time
Now substitute \( D = 2S \) back into the equation for \( T \):
\[ T = \frac{D}{S} = \frac{2S}{S} = 2 \text{ hours} \]

### Final Answer
The time taken to cover the distance with his normal speed is:
\[ \boxed{2 \text{ hours}} \]