A man rows at a speed of $2$ mph in still water. He sets out on a trip towards a spot $2$ miles downstream. He rows with the current until he is halfway there, then turns back and rows against the current for $15$ minutes. Then, he turns around again and rows with the current until he reaches his destination. The entire trip takes him $70$ minutes. The speed of the current can be represented as $\frac{p}{q}$ mph, where $p$ and $q$ are relatively prime positive integers. Find $10p + q$.

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