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
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.