There is one yacht starting at $(x_1,0)$ when $t=0$, which is sailing toward positive direction of $x$-axis with a constant velocity $b_1$, another yacht is starting at $(0,x_2)$ when $t=0$, and is always sailing toward the first yacht with a constant speed $b_2 > b_1$.
Question: Find the equation $u(x_1,x_2)$ satisfies, where $u(x_1,x_2)$ is the time that the second yacht catches up with the first yacht.
My thought was writing out two integral equations first, which show the relations of the total traveled distances in horizontal and vertical direction of those two yachts. $ \begin{aligned} \int^{u(x_1,x_2)}_0 b_2^{(x_1)}(t;x_1,x_2)\,dt &= x_1+ b_1 u(x_1,x_2) \\ \int^{u(x_1,x_2)}_0 b_2^{(x_2)}(t;x_1,x_2)\,dt &= x_2 \end{aligned} $ where $b_2^{(x_i)}(t)$ is the velocity $b_2$ in the direction $x_i$, but trying to differentiate with respect to $x_1$ and $x_2$ give me some weird looking results.