$A$ power boat and a raft both left dock $A$ on a river and headed downstream. The raft drifted at the speed of the river current. The power boat maintained a constant speed with respect to the river. The power boat reached dock $B$ downriver, then immediately turned and traveled back upriver. It eventually met the raft on the river $9 ~hours$ after leaving dock $A.$ If the answer is $x$ hours, what is the value of $10x$?

Let's think step by step and output the final answer within \boxed{}.
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