Prateek takes 8 hours to travel 36 km downstream and return to the same spot the speed of boat in still water is 12 km per hour find the speed of water current
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Let Downstream travel time=t h
Upstream travel time=(8-t)h
Downstream speed, Vd=36/t kmph
Upstream speed, Vu=36/(8-t)kmph
Speed of boat, Vb =12kmph
Water current speed, Vs=Vd-Vb...(1)
Also, Vu=Vb-Vs =>Vs=Vb-Vu... (2)
From (1)&(2),
Vd-Vb=Vb-Vu
2Vb=Vd-Vu
2*12=24=36{(1/t)-1/(8-t)}
2/3=1/t-1/(8-t)=(8-2t)/8t-t^2
16t-2t^2=24-6t
2t^2-22t+24=0
t^2-11t+12=0
t=
=1.2
So speed of water =Vd-Vb=36/1.2 - 12= 18kmph
Upstream travel time=(8-t)h
Downstream speed, Vd=36/t kmph
Upstream speed, Vu=36/(8-t)kmph
Speed of boat, Vb =12kmph
Water current speed, Vs=Vd-Vb...(1)
Also, Vu=Vb-Vs =>Vs=Vb-Vu... (2)
From (1)&(2),
Vd-Vb=Vb-Vu
2Vb=Vd-Vu
2*12=24=36{(1/t)-1/(8-t)}
2/3=1/t-1/(8-t)=(8-2t)/8t-t^2
16t-2t^2=24-6t
2t^2-22t+24=0
t^2-11t+12=0
t=
=1.2
So speed of water =Vd-Vb=36/1.2 - 12= 18kmph
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