A car travels 1/3 of the total distance to its destination at a speed of 30km/hr,and then travel the remaining distance at a speed of 40km/hr.if the car took 4hrs for the whole journey,what is the total distance of the journey?Give your answer in repeating decimal

Let $D$ be the total distance of the journey in km.
For the first part of the journey:
The distance covered is $D_1 = \frac{1}{3}D$.
The speed is $S_1 = 30 \text{ km/h}$.
The time taken for the first part is $T_1 = \frac{D_1}{S_1} = \frac{\frac{1}{3}D}{30} = \frac{D}{90}$ hours.

For the second part of the journey (remaining distance):
The remaining distance is $D_2 = D - D_1 = D - \frac{1}{3}D = \frac{2}{3}D$.
The speed is $S_2 = 40 \text{ km/h}$.
The time taken for the second part is $T_2 = \frac{D_2}{S_2} = \frac{\frac{2}{3}D}{40} = \frac{2D}{120} = \frac{D}{60}$ hours.

The total time for the whole journey is given as 4 hours.
So, $T_1 + T_2 = 4$.

$$\frac{D}{90} + \frac{D}{60} = 4$$

To solve for $D$, find the least common multiple (LCM) of the denominators 90 and 60.
The LCM$(90, 60) = 180$.
Multiply the entire equation by 180 to eliminate the denominators:

$$180 \left( \frac{D}{90} \right) + 180 \left( \frac{D}{60} \right) = 4 \times 180$$ $$2D + 3D = 720$$ $$5D = 720$$ $$D = \frac{720}{5}$$ $$D = 144 \text{ km}$$

Since 144 is an integer, it can be written as a repeating decimal by adding a decimal point and an infinite sequence of zeros.

$$D = 144.\overline{0} \text{ km}$$

The total distance of the journey is $\text{144.}\overline{\text{0}} \text{ km}$.