Please reason step by step, and put your final answer within \boxed{}.
A hiker is walking at a certain rate. She is passed by a cyclist traveling in the same direction along the same path at 15 miles per hour. The cyclist stops to wait for the hiker 5 minutes after passing her, while the hiker continues to walk at her constant rate. The cyclist must wait 13.75 minutes until the hiker catches up. What is the hiker's speed?
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