Question Number 30538 by SammyKT last updated on 23/Feb/18
$${A}\:{man}\:{rows}\:{a}\:{boat}\:{downstream} \\ $$$${for}\:\mathrm{3}\:{hours}\:{and}\:{then}\:{upstream} \\ $$$${for}\:\mathrm{3}\:{hours}.\:{If}\:{he}\:{covered}\:{a} \\ $$$${total}\:{distance}\:{of}\:\mathrm{12}{km},\:{find} \\ $$$${the}\:{speed}\:{of}\:{the}\:{water}\:{current}. \\ $$$$ \\ $$
Answered by mrW2 last updated on 24/Feb/18
$${if}\:{the}\:{water}\:{were}\:{still},\:{the}\:{man}\:{would} \\ $$$${come}\:{back}\:{to}\:{his}\:{starting}\:{point}\:{after} \\ $$$$\mathrm{6}\:{hours}.\:{that}\:{means}\:{the}\:{water}\:{moves} \\ $$$${him}\:\mathrm{12}\:{km}\:{in}\:\mathrm{6}\:{hours}.\:{the}\:{speed}\:{of} \\ $$$${water}\:{is}\:{hence}\:\mathrm{12}/\mathrm{6}=\mathrm{2}\:{km}/{h}. \\ $$
Commented by mrW2 last updated on 25/Feb/18
$$\mathrm{3}×\left({v}_{{m}} +{v}_{{w}} \right)−\mathrm{3}×\left({v}_{{m}} −{v}_{{w}} \right)=\mathrm{12} \\ $$$$\Rightarrow\mathrm{6}×{v}_{{w}} =\mathrm{12} \\ $$$$\Rightarrow{v}_{{w}} =\frac{\mathrm{12}}{\mathrm{6}}=\mathrm{2}\:{km}/{h} \\ $$