A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and…

Let x be the speed of the stream in km/hr.

1. Downstream speed = 15 + x km/hr; upstream speed = 15 - x km/hr.

2. Total time for 30 km each way: 30/(15 + x) + 30/(15 - x) = 4.5 hours.

3. Multiply both sides by (15 + x)(15 - x) = 225 - x^2 to clear denominators:

4. 30(15 - x) + 30(15 + x) = 4.5(225 - x^2).

5. Simplify the left side: 450 - 30x + 450 + 30x = 900, so 900 = 4.5(225 - x^2).

6. Compute 4.5 × 225 = 1012.5, so 900 = 1012.5 - 4.5 x^2. Rearranging gives 4.5 x^2 = 1012.5 - 900 = 112.5.

7. Therefore x^2 = 112.5 / 4.5 = 25, so x = 5 km/hr (taking the positive root for speed).

Final answer: 5 km/hr