The cruise ship

The cruise ship speeds 12 km/h at a calm surface. When we sailed 45 km along the river and 45 km back, it took us exactly 8 hours. Which (constant) speed of flow of the river?

Final Answer:

v =  3 km/h

Step-by-step explanation:

$$\begin{gathered} 45=t_1(12+v) \\ 45=(8-t_1)\cdot (12-v) \\ {t}_1=45/(12+v) \\ 45=(8-45/(12+v))\cdot (12-v) \\ 45\cdot (12+v)=(8\cdot (12+v)-45)\cdot (12-v) \\ 45\cdot (12+v)=(8\cdot (12+v)-45)\cdot (12-v) \\ 8v^2-72=0 \\ 8=2^3 \\ 0 \\ 72=2^3\cdot 3^2 \\ \text{GCD}(8,0,72)=2^3=8 \\ {v}^2-9=0 \\ {v}_{1,2}=\pm \sqrt{9}=\pm 3 \\ {v}_1=3 \\ {v}_2=-3 \\ v>0 \\ v=v_1=3=3\text{km/h} \\ {t}_1=45/(12+v)=45/(12+3)=3\text{h} \\ {t}_2=45/(12-v)=45/(12-3)=5\text{h} \end{gathered}$$

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