An employee, travelling at 20 km/h reaches his office half - an - hour late than the time he would take while travelling at 25 km/h . Find the distance between his house and the office

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Define Variables
Let the distance between the employee's house and office be \( D \) km.
Let the time taken to reach the office at a speed of 25 km/h be \( x \) hours.

### Step 2: Write the Time Equations
1. When traveling at 25 km/h, the time taken is \( x \) hours.
2. When traveling at 20 km/h, the time taken is \( x + \frac{1}{2} \) hours (since he is half an hour late).

### Step 3: Set Up the Distance Equation
Since distance is the same in both cases, we can set up the equation:
\[ D = \text{Speed} \times \text{Time} \]
For 25 km/h:
\[ D = 25 \times x \]
For 20 km/h:
\[ D = 20 \times \left(x + \frac{1}{2}\right) \]

### Step 4: Equate the Two Expressions for Distance
Now we can set the two expressions for \( D \) equal to each other:
\[ 25x = 20\left(x + \frac{1}{2}\right) \]

### Step 5: Simplify the Equation
Distributing the 20 on the right side:
\[ 25x = 20x + 10 \]

### Step 6: Solve for \( x \)
Now, isolate \( x \):
\[ 25x - 20x = 10 \]
\[ 5x = 10 \]
\[ x = 2 \text{ hours} \]

### Step 7: Find the Distance \( D \)
Now that we have \( x \), we can find the distance:
Using the equation \( D = 25x \):
\[ D = 25 \times 2 = 50 \text{ km} \]

### Final Answer
The distance between his house and the office is **50 km**.

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