Final answer:
When traveling downstream, the effective speed is the sum of the steamer's speed in still water and the speed of the stream, while when traveling upstream, the effective speed is the difference between the steamer's speed in still water and the speed of the stream. By setting up and solving an equation, we find that the speed of the steamer in still water is 10 km/h.
Step-by-step explanation:
To find the speed of the steamer in still water, we can use the concept of relative velocity. Let's assume the speed of the steamer in still water is 'x' km/h.
When the steamer is traveling downstream, its effective speed is the sum of its speed in still water and the speed of the stream. So, the effective speed is (x + 5) km/h.
When the steamer is traveling upstream, its effective speed is the difference between its speed in still water and the speed of the stream. So, the effective speed is (x - 5) km/h.
According to the problem, the time taken to travel 90 km downstream is the same as the time taken to travel 60 km upstream. Using the formula 'time = distance / speed', we can set up the following equation:
90 / (x + 5) = 60 / (x - 5)
Cross multiplying and simplifying the equation, we get:
90(x - 5) = 60(x + 5)
Solving for 'x', we find the speed of the steamer in still water is 10 km/h.
Therefore, the answer is (b) 10 km/h.