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Question Number 30538 by SammyKT last updated on 23/Feb/18

A man rows a boat downstream  for 3 hours and then upstream  for 3 hours. If he covered a  total distance of 12km, find  the speed of the water current.

$${A}\:{man}\:{rows}\:{a}\:{boat}\:{downstream} \\ $$$${for}\:\mathrm{3}\:{hours}\:{and}\:{then}\:{upstream} \\ $$$${for}\:\mathrm{3}\:{hours}.\:{If}\:{he}\:{covered}\:{a} \\ $$$${total}\:{distance}\:{of}\:\mathrm{12}{km},\:{find} \\ $$$${the}\:{speed}\:{of}\:{the}\:{water}\:{current}. \\ $$$$ \\ $$

Answered by mrW2 last updated on 24/Feb/18

if the water were still, the man would  come back to his starting point after  6 hours. that means the water moves  him 12 km in 6 hours. the speed of  water is hence 12/6=2 km/h.

$${if}\:{the}\:{water}\:{were}\:{still},\:{the}\:{man}\:{would} \\ $$$${come}\:{back}\:{to}\:{his}\:{starting}\:{point}\:{after} \\ $$$$\mathrm{6}\:{hours}.\:{that}\:{means}\:{the}\:{water}\:{moves} \\ $$$${him}\:\mathrm{12}\:{km}\:{in}\:\mathrm{6}\:{hours}.\:{the}\:{speed}\:{of} \\ $$$${water}\:{is}\:{hence}\:\mathrm{12}/\mathrm{6}=\mathrm{2}\:{km}/{h}. \\ $$

Commented by mrW2 last updated on 25/Feb/18

3×(v_m +v_w )−3×(v_m −v_w )=12  ⇒6×v_w =12  ⇒v_w =((12)/6)=2 km/h

$$\mathrm{3}×\left({v}_{{m}} +{v}_{{w}} \right)−\mathrm{3}×\left({v}_{{m}} −{v}_{{w}} \right)=\mathrm{12} \\ $$$$\Rightarrow\mathrm{6}×{v}_{{w}} =\mathrm{12} \\ $$$$\Rightarrow{v}_{{w}} =\frac{\mathrm{12}}{\mathrm{6}}=\mathrm{2}\:{km}/{h} \\ $$

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