A boat sails a distance of 44 km in 4 hours with the current. It takes 4 hours 48 minutes longer to cover the same distance against the current. Find the speed of the boat in still water and the speed of the current.

Let speed of boat in still water be x km/h and speed of current be y km/h.

Speed of boat in the current = (x + y) km/h

Speed of boat against current = (x - y) km/h

Given, boat takes 4 hours to go 44 km with the current

$\therefore \dfrac{44}{x + y} = 4$

⇒ 4(x + y) = 44

⇒ x + y = 11 …….(i)

Given, boat takes 4 hours 48 minutes longer

$\therefore \dfrac{44}{x - y} = 4 + 4 + \dfrac{48}{60} \\[1em] \Rightarrow \dfrac{44}{x - y} = 4 + 4 + \dfrac{4}{5} \\[1em] \Rightarrow \dfrac{44}{x - y} = \dfrac{20 + 20 + 4}{5} \\[1em] \Rightarrow \dfrac{44}{x - y} = \dfrac{44}{5} \\[1em] \Rightarrow x - y = \dfrac{44 \times 5}{44} \\[1em] \Rightarrow x - y = 5 …….(ii)$

Adding (i) and (ii) we get,

⇒ (x + y) + (x - y) = 11 + 5

⇒ 2x = 16

⇒ x = 8.

Substituting value of x in (i) we get,

⇒ 8 + y = 11

⇒ y = 3.

Hence, speed of boat in still water = 8 km/h and speed of current = 3 km/h.