Question

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

Answer 1

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 case when the boat goes 32km upstream ,let the time taken, in hour be t . 
then t = 32/x-y 
let the t be the timetaken by the boat to go down stream
 t =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 get 
y=2 
so ,speed of stillwater is10km /h and stream is 2km/h