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The speed of a stream is 3 km/hr. A boat goes 36 km and comes back to the starting point in 9 hours. What is the speed (in km/hr) of the boat in still water?

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The speed of a stream is 3 km/hr. A boat goes 36 km and comes back to the starting point in 9 hours. What is the speed (in km/hr) of the boat in still water?
1). 8
2). 9
3). 10
4). 7


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Answered by on | Votes 0 |

Speed of stream = a = 3 km/hr

Let speed of boat in still water be x km/hr

⇒ Speed upstream = x – 3

⇒ Speed downstream = x + 3

Total distance covered in 9 hours = 36 + 36 = 72 km

Time taken to go upstream = 36/(x – 3)

Time taken to go downstream = 36/(x + 3)

⇒ 36/(x + 3) + 36/(x – 3) = 9

⇒ 4/(x + 3) + 4/(x – 3) = 1

⇒ 4x + 12 + 4x – 12 = x2 - 9

⇒ x2 – 8x – 9 = 0

⇒ x = 9 or x = -1

∴ Speed of boat in still water = 9 km/hr as speed cannot be negative.

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