By walking at 3/4 of his usual speed a man reaches his office 20 min later than usual this usual time is

Options

A. 30min
B. 60min
C. 75 min
D. 1 hour 30 min

Answer

To solve the problem, we need to find the usual time it takes for the man to reach his office. Let's denote the following:

- Let \( x \) be the usual time taken to reach the office (in minutes).
- The usual speed of the man is \( v \).
- When he walks at \( \frac{3}{4} \) of his usual speed, his speed becomes \( \frac{3}{4}v \).

### Step 1: Establish the relationship between speed, distance, and time

The distance to the office can be expressed in two ways:

1. Using the usual speed:
\[ \text{Distance} = v \cdot x \]

2. Using the reduced speed:
\[ \text{Distance} = \left(\frac{3}{4}v\right) \cdot (x + 20) \]

### Step 2: Set the two distance expressions equal to each other

Since both expressions represent the same distance, we can set them equal to each other:
\[ v \cdot x = \left(\frac{3}{4}v\right) \cdot (x + 20) \]

### Step 3: Simplify the equation

We can cancel \( v \) from both sides (assuming \( v \neq 0 \)):
\[ x = \frac{3}{4}(x + 20) \]

### Step 4: Distribute and solve for \( x \)

Distributing \( \frac{3}{4} \):
\[ x = \frac{3}{4}x + 15 \]

Now, we can isolate \( x \):
\[ x - \frac{3}{4}x = 15 \]
\[ \frac{1}{4}x = 15 \]

### Step 5: Multiply both sides by 4 to find \( x \)

\[ x = 15 \cdot 4 = 60 \]

Thus, the usual time taken to reach the office is \( 60 \) minutes.

### Final Answer:
The usual time is **60 minutes**.

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