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Question
The speed of a boat in still water is 8km/h. It takes the same time in going 20km in downstream as it takes in going 12 km upstream. Find the speed of the stream.
Solution
Distance travelled downstream = 20 km.
Distance travelled upstream = 12 km.
Given, The speed of a boat in still water is 8km/h.
Let the speed of a boat in still water is 8km/h.
Let the speed of the stream = x km/hr.
Relative speed upstream = (8 - x) km/hr
Relative speed downstream = (8 + x) km/hr
Time taken to go upstream = `(12)/(8 - x)"hrs"`
Time taken to go downstream = `(20)/(8 - x)"hrs"`
As per given condition, boat takes the same time in going 20km in downstream as it takes in going 12km upstream.
⇒ `(12)/(8 - x) = (20)/(8 + x)`
12(8 + x) = 20(8 - x)
⇒ 12 x 8 + 12x = 20 x 8 - 20x
⇒ 8(20 - 12) = 32x
⇒ 64 = 32x
⇒ x = 2km/hr
Thus, the speed of the stream = 2 km/hr.
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