A hunter $($point H$)$ is at a point along a river bank. He wants to get to his cabin, located $3$ miles north and $10$ miles west $($point C $).$ He can travel $6$ mph along the river $($horizontally in the figure$)$ but only $2$ mph on the rocky land $($vertically in the figure$).$ How far upriver should he go in order to reach the cabin in minimum time?

The hunter should walk approximately $$ mi along the river.

$($Do not round until the final answer. Then round to the nearest tenth as needed.$)$