# 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.

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important 5 mark board question

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1. 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.

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