Question

A boat can cover 40km upstream and 60km down stream in 13hour.also it can cover 50km upstream and 72km downstream in 16hour.find the speed of boat still water

Answer 1

let the speed of river be X
and the speed of boat in still water be Y

speed in downstream will be X+Y
speed in upstream will be X-Y

we know that time = distance/speed

$\frac{40}{x - y} + \frac{60}{x + y} = 13$
this is eqn(1)
$\frac{50}{x - y} + \frac{72}{x + y} = 16$
this is eqn(2)

let
$\frac{1}{x - y} \: \: be \: a$
$\frac{1}{x + y} \: \: be \: b$
so
40a+60b=13 ......(3)
50a+72b=16.........(4)

in (3)
$a = \frac{13 - 60b}{40}$
by substituting value of a
$50( \frac{13 - 60b}{40} ) + 72b = 16$
$\frac{65 - 300b + 298b}{4} = 16$
$65 - 2b = 64$
$- 2b = - 1$
$b = \frac{ - 1}{ - 2}$
$b = \frac{1}{2}$

now a=
$a = \frac{13 - 60 \frac{1}{2} }{40}$
$a = \frac{13 - 30}{40}$
$a = \frac{ - 17}{40}$
we know
$a = \frac{1}{x - y}$
so
$x - y = \frac{ - 40}{17}$
this is eqn(£)
and
$b = \frac{1}{x + y}$
$x + y = 2$
this is eqn ($)
in ($)
X=2-y

$2 - y - y = \frac{ - 40}{17}$
$2 - 2y = \frac{ - 40}{17}$

$34 - 34y = - 40$
$- 34y = - 40 - 34$
$- 34y = - 74$

$y = \frac{ - 74}{ - 34}$
similarly by substituting value of y in ($) we get
$x + \frac{ - 74}{ - 34} = 2$
$x = 2 - \frac{37}{17}$
$x = \frac{ - 3}{17}$



may be there is a calculation error but the procedure will be same