Explanation

Let the distance between the police officer's house and office be D km.
Let the actual time required to reach the office on time be T hours.

Step 1: Forming Equations

Using the speed-time formula:

$$text{Time} = frac{text{Distance}}{text{Speed}}$$Speed​

Case 1: Walking at 4 km/h

D/4​​=T+5/60​

(since he is 5 minutes late, which is 5/60 hours)

Case 2: Walking at 5 km/h

D5​=T−10/60​

(since he is 10 minutes early, which is 10/60 hours)

Step 2: Solving for Distance

From the first equation:

T=D/4​−5/60​

From the second equation:

T=D/5​+10/60​

Equating both expressions for T:

D/4​−5/60​=D/5​+10/60​

Multiply everything by 60 to clear the fractions:

$$60 times left( frac{D}{4} - frac{5}{60} right) = 60 times left( frac{D}{5} + frac{10}{60} right)$$15D−5=12D+10
$$15D-12D=10+5$$$$3D = 15$$ $$D = 5 text{ km}$$

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