A person can complete a journey in 12 h. He travels the first half of the journey at a speed of 18 km/h and the second half at a speed of 30 km/h. Find the total journey in km.

Correct option is B

Given:

Total time for the journey = 12 hours

Speed for the first half of the journey = 18 km/h

Speed for the second half of the journey = 30 km/h

Formula Used:

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

Solution:

Let the total distance of the journey be D km. Since the journey is divided into two equal halves:

The distance for the first half =$$\frac{D}{2}$$​ km

The distance for the second half =$$\frac{D}{2}$$​ km

Time for the first half of the journey:

​$$\text{Time}_1 = \frac{\frac{D}{2}}{18}$$​​

Time for the second half of the journey:

​$$\text{Time}_2 = \frac{\frac{D}{2}}{30}$$​​

Total Time $$= \text{Time}_1 + \text{Time}_2$$​

$$12 = \frac{\frac{D}{2}}{18} + \frac{\frac{D}{2}}{30}$$​

​$$12 = \frac{5D}{180} + \frac{3D}{180}$$​

​$$12 = \frac{8D}{180}$$​

​$$12 \times 180 = 8D$$​

D $$= \frac{2160}{8} = 270$$​

The total distance of the journey is 270 km.