a boat covers 32km upstream and 36km downstream in 7hours. also it covers 40km upstream and 48km downstream in 9hours. find the speed of the boat in still water and that of stream?

speed of still water=x

speed of stream=y

speed of boat upstream=(x-y)km/h

speed of boat down stream=(x+y)km/h

also, time = distance/speed

in first casewhen the boat goes32km upstream ,let the time taken, in hour be t_{1}. then

t_{1}= 32/x-y

let the t_{2} be the timetaken by the boat to go down stream

t_{2}=36/x+y

so eq is 32/x-y +36/x+y=7

in second case the eq is

40/x-y+48/x+y=9

subsitute 1x-y=u ,1/x+y=v

so we get 32u +36v=7........... eq i

and 40u+48v=9

use elimination method to solve eq i and eq ii then we get,

v=1/12

u=1/8

1/x-y=u ,1/x-y=1/8

x-y =8 ..........eq 3

and x+y=12 eq 4

subtract both the eq we get

x=10

add both the eq we gt

y=2

so ,speed of stillwater is10km /h and stream is 2km/h