One-third of a certain distance was covered by a car at a speed of 30 km/h and the remaining distance was covered by the car at 20 km/h. How much distance was covered by the car in 4 hours?

Correct option is C

Given:

One-third of the distance = $$\frac{D}{3}$$​,at 30 km/h.

The remaining two-thirds of the distance =$$\frac{2D}{3},$$​at 20 km/h.

Solution:

Let the total distance be = D

One-third of the distance = $$\frac{D}{3}$$, at 30 km/h.

The remaining two-thirds of the distance = $$\frac{2D}{3},$$ at 20 km/h.

The time taken for each segment is: $$t_1$$ and $$t_2$$​​

$$t_1 = \frac{\frac{D}{3}}{30} = \frac{D}{90}$$ 

$$t_2 = \frac{\frac{2D}{3}}{20} = \frac{2D}{60} = \frac{D}{30}$$ 

The total time for the journey is:

$$t_{\text{total}} = t_1 + t_2$$

= $$\frac{D}{90} + \frac{D}{30}$$ = $$= \frac{D +3D}{90} = \frac{4D}{90} = \frac{2D}{45}$$ 

The total time is given as 4 hours thus:

$$\frac{2D}{45} = 4$$

$$2D = 4 \times 45$$ $$= \frac{180}{2} = 90 \, \text{km}$$ 

Thus the correct answer is (C)