A boat cover 32 km upstream and 36 km downstream in 7 hours . also ,it covers 40 km upstream and 48 km downstream in 9 hours . the speed of the boat in still water ?
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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 t1. then
t1= 32/x-y
let the t2 be the timetaken by the boat to go down stream
t2=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
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