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

Answer: 5 km/hr

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

Downstream speed = 15 + x km/hr. Upstream speed = 15 - x km/hr.

Time downstream = 30/(15 + x). Time upstream = 30/(15 - x). The total time is 4.5 hours.

Set up the equation:

30/(15 + x) + 30/(15 - x) = 4.5

• Multiply both sides by (15 + x)(15 - x) = 225 - x^2:

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

• Simplify the left side: 30*15 - 30x + 30*15 + 30x = 900.

• So 900 = (9/2)(225 - x^2). Multiply both sides by 2: 1800 = 9(225 - x^2).

• Expand and rearrange: 1800 = 2025 - 9x^2 ⇒ 9x^2 = 225 ⇒ x^2 = 25 ⇒ x = 5 (positive root).

Therefore the speed of the stream is 5 km/hr.