A bus covers 30% of a journey at a speed of 24 km/h and the remaining distance at a speed of 36 km/h. What is the average speed of the bus for the entire journey?

The correct answer is 31.3 km/h.

To find the average speed of the bus for the entire journey, we use the standard formula:
$\text{Average Speed}=\frac{\text{Total Distance}}{\text{Total Time}}$
Let us assume the total distance of the journey is $D$ km.

Step 1: Find the distance and time for the first portion of the journey.
The bus covers 30% of the total distance at a speed of 24 km/h.
Distance for part 1 ($d_1$):
$d_1=30\%\text{of}D=\frac{3D}{10}\text{km}$
Time taken for part 1 ($t_1$):
$t_1=\frac{d_1}{{\text{Speed}}_1}=\frac{\frac{3D}{10}}{24}=\frac{3D}{240}=\frac{D}{80}\text{hours}$

Step 2: Find the distance and time for the remaining portion of the journey.
The remaining distance is 100% - 30% = 70% of the total distance, covered at a speed of 36 km/h.
Distance for part 2 ($d_2$):
$d_2=70\%\text{of}D=\frac{7D}{10}\text{km}$
Time taken for part 2 ($t_2$):
$t_2=\frac{d_2}{{\text{Speed}}_2}=\frac{\frac{7D}{10}}{36}=\frac{7D}{360}\text{hours}$

Step 3: Calculate total time taken.
Total time ($T$):
$T=t_1+t_2=\frac{D}{80}+\frac{7D}{360}$
Taking the least common multiple (LCM) of 80 and 360, which is 720:
$T=\frac{9D+14D}{720}=\frac{23D}{720}\text{hours}$

Step 4: Compute the average speed.
Substitute total distance $D$ and total time $T$ into the average speed formula:
$\text{Average Speed}=\frac{D}{\frac{23D}{720}}=\frac{720}{23}\approx 31.3\text{km/h}$

Thus, the average speed of the bus for the entire journey is approximately 31.3 km/h.