A boat requires 6 hrs to travel 36 km downstream and 24 km upstream. It requires 9 hrs to travel 48 km down

Answer: Speed of boat in still water = 10 km/hr, speed of stream = 2 km/hr

Let the speed of the boat in still water be \(x\) km/hr and of the stream \(y\) km/hr.

Downstream speed = \(x + y\), upstream speed = \(x - y\). Since time = distance/speed:

\[\frac{36}{x + y} + \frac{24}{x - y} = 6,\qquad \frac{48}{x + y} + \frac{40}{x - y} = 9\]

Put \(p = \dfrac{1}{x + y}\) and \(q = \dfrac{1}{x - y}\):

\[36p + 24q = 6 \Rightarrow 6p + 4q = 1 \quad\text{(1)}\]

\[48p + 40q = 9 \quad\text{(2)}\]

Multiply (1) by 10: \(60p + 40q = 10\). Subtract (2): \(12p = 1 \Rightarrow p = \dfrac{1}{12}\).

From (1): \(\dfrac12 + 4q = 1 \Rightarrow q = \dfrac18\).

So \(x + y = 12\) and \(x - y = 8\). Adding: \(2x = 20 \Rightarrow x = 10\), and \(y = 2\).

Check: 36/12 + 24/8 = 3 + 3 = 6 hr and 48/12 + 40/8 = 4 + 5 = 9 hr.