Speed of a boat in still water is 15 km/h. It goes 30 km upstream and returns back at the same point in 4 hours 30 minutes. Find the speed of the stream.

Given: Speed of boat in still water = 15 km/hr.

Let the speed of stream = x km/hr.

Distance covered by boat in going upstream = Distance covered by boat in downstream = 30 km

Speed of boat upstream = Speed of boat in still water – Speed of stream = (15 - x) km/hr.

Speed of boat downstream = Speed of boat in still water + Speed of stream = (15 + x) km/hr.

Since, Distance = Speed × Time

⇒ Time = Distance / Speed

Time taken by boat upstream =

Time taken by boat downstream

Total time taken by the boat to go and come back to the same point = 4.5 hrs.

∴

Multiply and divide both sides by (15 - x)(15 + x):

⇒ 4.5 (225 – x²) = 30(15 + x) + 30(15 - x)

⇒ 1012.5 – 4.5x² = 450 + 30x + 450 – 30 x

⇒ 1012.5 – 4.5x² = 900

⇒ 4.5x² = 112.5

⇒ x² = 25

⇒ x = 5

But speed can’t be negative, ∴ Speed of the stream = 5 km/hr.