A boat travels a distance of 12 km. The first 4 km along the stream is covered in 15 minutes. The next 8 km is upstream. The downstream speed is twice the upstream speed. What is the average speed for the journey?

Correct option is D

Solution:

Let the upstream speed be x km/h.

According to the problem, the downstream speed is twice the upstream speed, so downstream speed = 2x km/h.
We are given:
Distance downstream (first 4 km) is covered in 15 minutes. Converting to hours, we have $$\frac{15}{60} = 0.25$$​ hours.
Using the formula  $$\text{Speed} = \frac{\text{Distance}}{\text{Time}}$$​, the downstream speed is:
​$$2x = \frac{4}{0.25}$$​​
This simplifies to:
​$$2x = 16 \Rightarrow x = 8 \, \text{km/h}$$​​
Therefore, the upstream speed is 8 km/h, and the downstream speed is 16 km/h.
Now, time taken for the upstream journey of 8 km is:
​$${Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{8}{8} = 1 \, \text{hour}$$​​
Total time taken for the entire journey is:
​$$\text{Total Time} = 0.25 + 1 = 1.25 \text{ hours}$$​​
The total distance traveled is 12 km, so the average speed is:
Average Speed = $$\frac{\text{Total Distance}}{\text{Total Time}} = \frac{12}{1.25} = 9.6 \text{ km/h}$$​​
Hence, the average speed for the journey is 9.6 km/h.