A motor boat moving at 9 km/hr in still water goes 12 km downstream and comes back in total of 3 hr. determine the speed of water.
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Speed of boat=9 kmph, Speed of stream=y kmph
Upstream speed = 9-y.... Up dist=12km
Downstream speed=9+y... Down dist=12km
Given,total time for upstream and downstream=3 hrs
12/9-y + 12/9+y = 3
[Trial and error or assuming, y=3 satisfies the equation. One can also solve it using quadratic equation]
y=speed of water=3kmph [check: 12/6 + 12/12 = 3hrs]
Quadratic method(expansion by lcm):
12/9-y + 12/9+y =3
12* [ 1/9-y + 1/9+y ] =3
(9+y+9-y)/(9-y)*(9+y) =1/4
18/(81-y^2) = 1/4
72= 81-y^2
y^2=9
y=3kmph
Upstream speed = 9-y.... Up dist=12km
Downstream speed=9+y... Down dist=12km
Given,total time for upstream and downstream=3 hrs
12/9-y + 12/9+y = 3
[Trial and error or assuming, y=3 satisfies the equation. One can also solve it using quadratic equation]
y=speed of water=3kmph [check: 12/6 + 12/12 = 3hrs]
Quadratic method(expansion by lcm):
12/9-y + 12/9+y =3
12* [ 1/9-y + 1/9+y ] =3
(9+y+9-y)/(9-y)*(9+y) =1/4
18/(81-y^2) = 1/4
72= 81-y^2
y^2=9
y=3kmph
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