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Either hobo can run to the other end of the flatcar and jump off with the same speed $u$ (relative to the car).

Use conservation of momentum to find the speed of the recoiling car if the two men run and jump off simultaneously.

Let $v$ be the velocity of the recoiling car.

Then

\begin{alignat*}{3}

m_{\text{fc}}v & = & 2m_{\text{h}}(u - v)\\

v & = & \frac{2m_{\text{h}}}{m_{\text{fc}}}(u - v)

\end{alignat*}

The solution is $v = \frac{2m_{\text{h}}}{2m_{\text{h}}+m_{\text{fc}}}u$.

How did they get that?