A train travels at a speed of $30\text{km/hour}$ for $12$ minutes and then for the next $8$ minutes at a speed of $45\text{km/hour}$. The average speed for the entire journey is:

To find the average speed, we calculate the total distance traveled divided by the total time taken.
Convert time intervals into hours:

$$t_1=12\text{ minutes}=\frac{12}{60}\text{ hour}=\frac{1}{5}\text{ hour}$$

$$t_2=8\text{ minutes}=\frac{8}{60}\text{ hour}=\frac{2}{15}\text{ hour}$$

Calculate the distances covered in each interval:

$$d_1={\text{speed}}_1\times t_1=30\times \frac{1}{5}=6\text{km}$$

$$d_2={\text{speed}}_2\times t_2=45\times \frac{2}{15}=6\text{km}$$

Calculate total distance and total time:

$$\text{Total Distance}=d_1+d_2=6+6=12\text{km}$$

$$\text{Total Time}=12+8=20\text{ minutes}=\frac{20}{60}\text{ hour}=\frac{1}{3}\text{ hour}$$

Now evaluate the average speed:

$$\text{Average Speed}=\frac{\text{Total Distance}}{\text{Total Time}}=\frac{12}{\frac{1}{3}}=12\times 3=36\text{km/hour}$$