Walking 6/7 of his usual speed, a man is 24 minutes late. The usual time taken by him to cover that distance is

Options

A. 136 min
B. 144 min
C. 140 min
D. 130 min

Answer

To solve the problem, we need to determine the usual time taken by the man to cover the distance when he walks at his normal speed. Let's break down the solution step by step:

### Step 1: Understand the relationship between speed, time, and distance.
The relationship between speed (S), time (T), and distance (D) is given by the formula:
\[ D = S \times T \]
This means that if the distance is fixed, then speed and time are inversely proportional.

### Step 2: Define the variables.
Let:
- \( S \) = Usual speed of the man
- \( T \) = Usual time taken to cover the distance
- The distance \( D \) can be expressed as \( D = S \times T \).

### Step 3: Calculate the new speed.
The man walks at \( \frac{6}{7} \) of his usual speed, so his new speed is:
\[ \text{New Speed} = \frac{6}{7} S \]

### Step 4: Calculate the time taken at the new speed.
The time taken to cover the same distance at the new speed is:
\[ \text{New Time} = \frac{D}{\text{New Speed}} = \frac{D}{\frac{6}{7} S} = \frac{7D}{6S} \]

### Step 5: Relate the new time to the usual time.
According to the problem, the man is 24 minutes late when walking at the new speed. Therefore, we can express this relationship as:
\[ \text{New Time} = T + 24 \]

### Step 6: Substitute the expression for new time.
Substituting the expression for new time into the equation gives:
\[ \frac{7D}{6S} = T + 24 \]

### Step 7: Substitute \( D \) in terms of \( T \).
We know that \( D = S \times T \), so we can substitute \( D \) in the equation:
\[ \frac{7(S \times T)}{6S} = T + 24 \]
This simplifies to:
\[ \frac{7T}{6} = T + 24 \]

### Step 8: Solve for \( T \).
To eliminate \( T \) from the right side, we can rearrange the equation:
\[ \frac{7T}{6} - T = 24 \]
\[ \frac{7T - 6T}{6} = 24 \]
\[ \frac{T}{6} = 24 \]
Multiplying both sides by 6 gives:
\[ T = 144 \]

### Conclusion
The usual time taken by the man to cover the distance is **144 minutes**.