A boat goes 8 km upstream and 12 km downstream in 7 hours. It goes 9 km upstream and 18 km downstream in 9 hours. What is the speed (in km/…

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

Speed of boat upstream = x - y

Speed of boat downstream = x + y

According to question,

{8/(x - y)} + {12/(x + y)} = 7

⇒ 8x + 8y + 12x - 12y = 7(x2 - y2)

⇒ 20x - 4y = 7(x2 - y2) ----(1)

Also,

{9/(x - y)} + {18/(x + y)} = 9

⇒ x + y + 2x - 2y = (x2 - y2)

⇒ 3x - y = (x2 - y2)

⇒ 21x - 7y = 7(x2 - y2) ----(2)

Subtracting equation (1) from (2) we get,

⇒ x - 3y = 0

⇒ x = 3y

Now, from equation (1) we get,

⇒ 60y - 4y = 7(9y2 - y2)

⇒ 56y = 56y2

⇒ y(y - 1) = 0

⇒ y = 1

Now,

⇒ x = 3y = 3 × 1 = 3 km/hr

∴ the speed of the boat in still water = 3 km/hr