A police officer walk from his house at 4 km per hour and reached his office 5 min late if his speed is 5 km per hour he will reach his office 10 min early. how far is his office from the house ?

5 km

5/12 km

2.5 km

10 km

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

$= T +$

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

Case 2: Walking at 5 km/h

$D5 = T -1 0/6 0$

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

Step 2: Solving for Distance

From the first equation:

$T =$

From the second equation:

$T =$

Equating both expressions for T:

D $=$

Multiply everything by 60 to clear the fractions:

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