Final answer:
The speed of the boat in still water is 6 km/h.
Step-by-step explanation:
To find the speed of the boat in still water, we can use the concept of relative velocity. Let's assume the speed of the boat in still water is x km/h.
When the boat is traveling upstream, it is moving against the current, so its effective speed is (x - 3) km/h. The distance covered is 4 km, so the time taken is 4/(x - 3) hours.
When the boat is traveling downstream, it is moving with the current, so its effective speed is (x + 3) km/h. The distance covered is 10 km, so the time taken is 10/(x + 3) hours.
Since the boat takes the same time for both upstream and downstream journeys, we can set up an equation:
4/(x - 3) = 10/(x + 3)
By cross-multiplying and solving the equation, we find that the speed of the boat in still water is 6 km/h.