Question

A boat covers 32km upstream and 36 km downstream in 7 hours. Also, it covers 40km upstream and 48km downstream in 9hours. Find the speed of still water and that of the stream.

Answer 1

let speed of boat in still water be x km/h and speed of stream be y km/hr
upstream speed of boat= (x-y) km/hr
and down stream speed of boat = (x+ y) km/hr
$time \: taken \: to \: go \: 32km \: upstream = \frac{32}{x - y} \\ time \: taken \: to \: go \: 36km \: downstream = \frac{36}{x + y} \\ according \: to \: 1st \: condition \\ \frac{32}{x - y} + \frac{36}{x + y} = 7$
similarly second condition
$\frac{40}{x - y} + \frac{48}{x + y} = 9$
$\frac{40}{x - y} + \frac{48}{x + y} = 9 \\ now \: put \: \frac{1}{x - y} = p \: and \: \frac{1}{x + y} = q \\ we \: get \\ 32p + 36q = 7 \\ 40p + 48q = 9$
solve these 2 equations and find the value of p and q and hence find x and y.

Answer 2

let speed of boat = x km/hr
let speed of stram = y km/hr

upstream =(x-y)km/hr
downstream =(x+y)km/hr

CASE 1: Speed = Distance/ Time
so , Time = Distance / Speed

30/x-y + 36/x+y = 7 eqn (1)

similarly

CASE 2: 40/x-y + 48/x+y = 9 eqn (2)

let 1/x-y =a and 1/x+y = b

Now putting value in eqn (1) and (2) , then
equations will be :

30a + 36b = 7 or 30a + 36b - 7 = 0
eqn (3)
40a + 48b = 9 or 40a + 48b - 9 = 0
eqn (4)

Solving eqn (3) and (4) by cross multiplication method , then

x y 1
b1 c1 a1 b1
b2 c2 a2 b2

x y 1
________ = __________ = _________

b1c2-b2c1 c1a2-c2a1 a1b2-a2b1


x y 1
________= _________ = _________

12 -10 1

x/12=1,,,,,,, so x= 12
similarly y = -10