Answer:
[tex]The\ velocity\ of\ a\ river\ flow=15\ km/h\\The\ velocity\ of\ the\ ship\ in\ stagnant\ water=3\ km/h[/tex]
Step-by-step explanation:
[tex]We\ are\ given\ that,\\Speed\ of\ the\ ship\ in\ the\ direction\ of\ water=18\ km/h\\Speed\ of\ the\ ship\ against\ the\ direction\ of\ the\ river=12\ km/h\\Now,\\First,\\Lets\ find\ the\ velocity\ of\ the\ river\ flowing.\\Lets\ consider\ that\ the\ river\ flows\ with\ a\ constant\ velocity\ of\ v\ km/h.\\\\We\ know\ that,\ the\ velocity\ of\ the\ river\ will\ actually\ be\ the\ velocity\ of\\ the\ ship\ flowing\ along\ with\ the\ river,\ when\ it\ doesn't\ actually\ propel\\ or\ accelerate.\\[/tex]
[tex]Hence,\\For\ Simplicity,\\v+F=18\ [When\ glides\ through\ the\ river]\\v-F=12\ [When\ glides\ against\ the\ river]\\Hence,\ by\ adding\ the\ two\ equations:\\(v+F)+(v-F)=18+12\\2v=30\\v=\frac{30}{2}=15\ km/h\\Note:\ The\ F\ stands\ for\ the\ speed\ of\ the\ ship\ independent\ of\ the\ river's\\ flow.[/tex][tex]Now,\\Lets\ consider\ the\ velocity\ of\ the\ ship\ when\ the\ river\ doesn't\ really\ flow.\\We\ already\ know\ that,\\Velocity\ of\ the\ ship\ in\ the\ direction\ of\ the\ river\ flow=18\ km/h\\Velocity\ of\ the\ ship\ against\ the\ direction\ of\ the\ river\ flow=12\ km/h\\Lets\ again\ refer\ to\ our\ first\ equation:\\v+F=18\\Hence,\\Substituting\ v=15,\\15+F=18\\F=18-15\\F=3\ km/h[/tex]
