Question

A boat can go 20 km upstream and 30 km downstream in 3 hrs. It can go 20 downstream and 10km upstream in 1 hrs 40 min . Find the speed of the boat in still water and speed of the stream.

Answer 1

Let the speed of the boat in still water be x kh/hr. and the speed of the stream be y km/hr.
Steam are boat is going upstream, the stream opposes the boat.
$\therefore$ Effective speed = (x-y) km/hr.
When the boat is going downstream, the stream helps the boat.
$\therefore$ Effective speed = (x+y) km/hr.
The boat travels 20 km upstream & 30 km downstream in 3 hours
$Time=\frac{distance}{speed}$
$\therefore \frac{20}{(x-y)}+\frac{20}{x+y}=3$ ---(i)
The total travels 20 km downstream of 10 km upstream in 1 hr . 40 mins, i.e., '
1.$\frac{2}{3}hours=\frac{5}{3}hours$
$\therefore \frac{20}{(x-y)}+\frac{20}{x+y}=\frac{5}{3}$ ---- (2)
(Equn (i) )1 – (equn (2) 2,
$\frac{20}{x-y}+\frac{30}{x+y}-\frac{20}{x-y}-\frac{40}{x+y}=3-\frac{10}{3}$
$\frac{-10}{x+y}=\frac{-1}{3}\Rightarrow x+y=30$ -----(3)
Substitute (3) in (1) $\frac{20}{x-y}+\frac{30}{30}=3$
$\therefore \frac{20}{x-y}=2\Rightarrow x-y=10$ ----- (4)

Equn (3) + equn (4)
x+y+x-y=30+10
X= 40
x=20 km/hr
x+y=30
$\therefore$ y= 30-x
= 30-20
y= 10 km/hr