Let the speed of stream be x speed in downstream - d/s - 30/15+x speed in upstream - d/s - 30/15-x total time - d/s - 30/(15+x)+30/(15-x) - 9/2. (time has been converted into hour.

Problem:
A motor boat, whose speed is 15 km/h in still water, goes 30 km downstream and comes back in a total of 4 hours 30 minutes. Determine the speed of the stream.

Solution:
Let's assume the speed of the stream is x km/h.

Time taken downstream:
The speed of the boat in still water is 15 km/h, and the speed of the stream is x km/h. So, the effective speed downstream will be (15 + x) km/h. The distance traveled downstream is 30 km. We can use the formula:
Time = Distance / Speed

The time taken downstream will be:
Time_downstream = 30 / (15 + x) hours

Time taken upstream:
The speed of the boat in still water is 15 km/h, and the speed of the stream is x km/h. So, the effective speed upstream will be (15 - x) km/h. The distance traveled upstream is also 30 km. We can use the formula:
Time = Distance / Speed

The time taken upstream will be:
Time_upstream = 30 / (15 - x) hours

Total time taken:
According to the problem, the total time taken for the round trip (downstream and upstream) is 4 hours 30 minutes, which is equivalent to 4.5 hours.

The total time taken will be:
Total time = Time_downstream + Time_upstream
4.5 = 30 / (15 + x) + 30 / (15 - x)

Solving the equation:
To solve the equation, we need to get rid of the denominators.

Multiplying the equation by (15 + x)(15 - x) will eliminate the denominators:
4.5(15 + x)(15 - x) = 30(15 - x) + 30(15 + x)

Now, let's simplify the equation:
4.5(225 - x^2) = 450 - 30x + 450 + 30x

Expanding and simplifying further:
1012.5 - 4.5x^2 = 900

Moving all terms to one side:
4.5x^2 = 112.5

Dividing both sides by 4.5:
x^2 = 25

Taking the square root of both sides:
x = ±5

Since the speed of the stream cannot be negative, the speed of the stream is 5 km/h.

Conclusion:
The speed of the stream is 5 km/h.