A cyclist leaves the town of Alphaville and heads toward Betaville. She travels at a constant speed of \(14\) km/h.
At the same time, a jogger and a walker leave Betaville and head toward Alphaville. The walker travels at a constant speed of \(6\) km/h and the jogger travels at a constant speed of \(10\) km/h.
If the cyclist passes the walker \(4\) minutes after passing the jogger, how far apart are the towns Alphaville and Betaville?