Question

A boat covers 32 km upstream and 36 km downstream in 7 h. also, it covers 40 km upstream and 48 km downstream in 9 h. 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