The problem asks us to find the distance between home and office, given that walking at 4 km/h takes 30 minutes longer than walking at 5 km/h.

1. Problem Description

The problem asks us to find the distance between home and office, given that walking at 4 km/h takes 30 minutes longer than walking at 5 km/h.

2. Solution Steps

Let $d$ be the distance between the house and the office in kilometers.

Let $t_1$ be the time it takes to walk at 4 km/h, and $t_2$ be the time it takes to walk at 5 km/h.

We are given that $t_1 = t_2 + 30 \text{ minutes}$. We need to convert the minutes into hours by dividing by 60, thus

$t_1 = t_2 + \frac{30}{60} = t_2 + \frac{1}{2}$ hours.

We know that distance = speed * time, so we have:

$d = 4t_1$

$d = 5t_2$

From the first equation, we have $t_1 = \frac{d}{4}$.

From the second equation, we have $t_2 = \frac{d}{5}$.

Substituting these into the equation $t_1 = t_2 + \frac{1}{2}$, we get

$\frac{d}{4} = \frac{d}{5} + \frac{1}{2}$

Multiplying both sides by 20, we get:

$5d = 4d + 10$

$5d - 4d = 10$

$d = 10$

Therefore, the distance between the house and the office is 10 km.

3. Final Answer

The distance between my house and office is 10 km.