Final answer:
The speed of the steamer in still water is found by setting the distance covered downstream and upstream equal to each other, taking into account the speed of the stream. The speed of the steamer in still water is 18 km/h, which corresponds to option C.
Step-by-step explanation:
To find the speed of the steamer in still water, we can use the concept of relative speed in moving fluids. The downstream speed of the steamer is the sum of its speed in still water and the speed of the stream, while the upstream speed is the difference between the steamer's speed in still water and the speed of the stream. Let's denote the speed of the steamer in still water as S km/h.
Going downstream, the overall speed is S + 2 km/h (since the stream speed is 2 km/h). If the steamer covers the distance between the two ports in 4 hours, we can write this as:
Distance = (S + 2) * 4
Going upstream, the overall speed is S - 2 km/h. If the same distance is covered in 5 hours, we can write:
Distance = (S - 2) * 5
Since both equations represent the same distance, we can set them equal to each other:
(S + 2) * 4 = (S - 2) * 5
Solving the equation, we get:
4S + 8 = 5S - 10
5S - 4S = 8 + 10
S = 18 km/h