A person can complete a journey in 24 hours. He covers the first one-third part of thejourney at the rate of 42 km/h and the remaining distance at the rate of 12 km/h. What isthe total distance(km) of his journey?

Correct option is A

Given:

Total time for the journey = 24 hours

The first one-third of the journey is covered at a speed of 42 km/h.

The remaining two-thirds of the journey is covered at a speed of 12 km/h.

Formula Used:

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

Solution:

Let the total distance be D 

Now, 

​$$\frac{D/3}{42}+\frac{2D/3}{12} = 24$$​​

​$$\frac{D}{126} + \frac{D}{18} = 24$$ 

​$$​\frac{D+7D}{126} = 24$$​​

​$$\frac{8D}{126} = 24$$​​

​$$\frac{4D}{63} = 24$$​​

​$$\implies D = \frac{24 \times 63}{4} = 378$$​​

Thus, the total distance of the journey is 378 km.