# Finding an equation to solve for the velocity of a swimmer crossing a river [closed]

Where $\theta=45^\circ$, $d_1=200\:\mathrm{m}$, and $d_2=150\:\mathrm{m}$. I do not know how to combine the following equations: \begin{align} t&=\frac{d_1}{v_s\cos(45^\circ)}\\ t&=\frac{d_2}{v_r-v_s \sin(45^\circ)} \end{align} Now these equation are equal to each other, but I do not know how to combine them to create an equation that solves for $v_s$. What is the process to find this equation?

## closed as off-topic by Brandon Enright, Abhimanyu Pallavi Sudhir, jinawee, John Rennie, DilatonMar 2 '14 at 10:10

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You just have to consider that t is the time to reach B, which satisfies both equations: $$t=\frac{d_1}{v_s.cos(45°)}=\frac{d_2}{v_r-v_s.sin(45°)}$$ $$\Leftrightarrow d_2.v_s.cos(45°)=d_1.(v_r-v_s.sin(45°))$$ $$\Leftrightarrow v_s.(d_2.cos(45°)+d_1.(sin(45)))=d_1.v_r$$ $$\Leftrightarrow v_s=\frac{d_1.v_r}{d_2.cos(45°)+d_1.(sin(45))}$$