A person can complete a journey in 13 hours. He covers the first one-third part of the journey at the rate of 24 km/h and the remaining distance at the rate of 60 km/h. What is the total distance of his journey?

Correct option is D

Given:

Total time for the journey = 13 hours

Speed for the first one-third of the journey = 24 km/h

Speed for the remaining two-thirds of the journey = 60 km/h

Formula Used:

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

Solution:
Let the total distance be D km.

For the first one-third of the journey, the distance is $$\frac{D}{3}.$$​​
The time taken for the first part of the journey =$$\frac{\frac{D}{3}}{24} = \frac{D}{72}$$​ hours.

For the remaining two-thirds of the journey, the distance is $$\frac{2D}{3}.$$​​
The time taken for the remaining part of the journey =$$\frac{\frac{2D}{3}}{60} = \frac{2D}{180}$$​ hours.

The total time for the journey is the sum of the time for both parts:

$$\frac{D}{72} + \frac{2D}{180} = 13 \\ \ \\\frac{5D}{360} + \frac{4D}{360} = 13 \\ \ \\\frac{9D}{360} = 13 \\ \ \\9D = 13 \times 360 \\ \ \\D = \frac{4680}{9} = 520 \, \text{km}$$​

Thus, the total distance of the journey is 520 km.