Question

⭐the speed of the boat in still water is 15km/h.it takes 4 1/2 hours to travel 30 km down the stream and back to the starting point. Find the speed of the stream.⭐

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Answer 1

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Answer 2

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

Given that Speed of the boat in still water is 15 km/hr.

⇒ Speed of the boat downstream = (15 + x) km/hr.

⇒ Speed of the boat upstream = (15 - x) km/hr.

We know that Time = (Distance/Speed).

According to the given information,

Time taken for upstream + Time taken for downstream = 4 (1/2) hours.

⇒ (30/15 + x) + (30/15 - x) = 4 1/2

⇒ (30/15 + x) + (30/15 - x) = 9/2

⇒ 2[30(15 + x) * 30(15 - x)] = 9(15 + x)(15 - x)

⇒ 2[450 + 30x + 450 - 30x] = 9(225 - x^2)

⇒ 2[900] = 2025 - 9x^2

⇒ 1800 - 2025 = -9x^2

⇒ -225 = -9x^2

⇒ x^2 = 25

⇒ x = √25

⇒ x = 5.

Therefore, Speed of the stream = 5 km/hr.

Hope this helps!