A boat goes 20 km upstream and 22 km downstream in 6 hours. Also, it goes 25 km upstream and 33 km downstream in 8 hours. What is the speed of the boat in still water and that of the stream ?
Answer & explanation
Correct answer: option 3
The correct answer is option (3) : Boat in still water = 8 km/hr and speed of stream = 3 km/hr
Let the speed of the boat in still water be x km/hr and speed of current be y km/hr then
downstream speed = (x + y) km/hr
upstream speed = (x-y) km/hr
Acc to given,
$\frac{20}{x-y}+\frac{22}{x+y}= 6$
$21x-y=3(x^2-y^2)$ ...............(i)
$\frac{25}{x-y}+\frac{33}{x+y}= 8$
$\frac{25(x+y)+33(x-y)}{(x-y)(x+y)}=8$
$29x-4y=4(x^2-y^2)$ .............(ii)
$(ii) ÷(i)$
$\frac{29x-4y}{21x-y}=\frac{4(x^2-y^2)}{3(x^2-y^2)}$
$3(29x-4y)= 4(21x-y)$
$x=\frac{8}{3}y$
Put $ x=\frac{8}{3}y $ in eq (i)
We get $ y = 0, 3 $ (But y ≠ 0)
At $y = 3 $ (speed of current)
$x= 8 $ (speed of boat)