A car completes a journey in 10 minutes. For the first half of the distance, the speed was 60 km/h and for the second half, the speed was 40 km/h. We need to find the total distance of the journey.

1. Problem Description

A car completes a journey in 10 minutes. For the first half of the distance, the speed was 60 km/h and for the second half, the speed was 40 km/h. We need to find the total distance of the journey.

2. Solution Steps

Let $d$ be the total distance of the journey in kilometers.

The time taken for the first half of the distance is $t_1 = \frac{d/2}{60}$ hours.

The time taken for the second half of the distance is $t_2 = \frac{d/2}{40}$ hours.

The total time is given as 10 minutes, which is equal to $\frac{10}{60} = \frac{1}{6}$ hours.

Therefore, $t_1 + t_2 = \frac{1}{6}$.

Substituting the expressions for $t_1$ and $t_2$, we get:

$\frac{d/2}{60} + \frac{d/2}{40} = \frac{1}{6}$

$\frac{d}{120} + \frac{d}{80} = \frac{1}{6}$

To solve for $d$, we first find a common denominator for the fractions on the left side. The least common multiple of 120 and 80 is

2

4

0. $\frac{2d}{240} + \frac{3d}{240} = \frac{1}{6}$

$\frac{5d}{240} = \frac{1}{6}$

$5d = \frac{240}{6}$

$5d = 40$

$d = \frac{40}{5}$

$d = 8$

3. Final Answer

The total distance of the journey is 8 km.