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Akshara was travelling in her boat when the wind blew her hat and hat started floating back stream. The boat continued to travel upstream for twelve minutes after which Akshara realized that her hat had fallen off and turned back downstream. She caught up with that as soon as it reached the starting point. Find the speed of river if Akshara’s hat flew off exactly 3 km from where she started?

Akshara was travelling in her boat when the wind blew her hat and hat started floating back stream. The boat continued to travel upstream for twelve minutes after which Akshara realized that her hat had fallen off and turned back downstream. She caught up with that as soon as it reached the starting point. Find the speed of river if Akshara’s hat flew off exactly 3 km from where she started? Correct Answer 7.5 km/hr

Let x km/hr be the speed of boat and y km/hr be the speed of stream

D be the total distance covered in 12 minutes together by hat and Akshara when Akshara realized that her at had fallen off

Here, the speed of the hat will be equal to speed of stream 

As the hat and Akshara are travelling in the opposite direction for 12 minutes before realization and Akshara is travelling upstream

D = 12y/60 + 12(x - y)/60

⇒ D = 12x/60

Now, Akshara realised that her hat is fallen off return in the downstream to take his hat

Akshara and hat are moving in the same direction and the distance between them is D so Akshara will catch the hat at the stating point in 

⇒ 12x/60/(x + y - y)

⇒ 12 minutes

Total distance covered by hat to reach the staring point is 3 km 

Total time taken to reach the starting point = 12 minutes + 12 minutes = 24 minutes

⇒ speed of stream = 3/(24/60) = 7.5 km/hr 

 

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