It looks like around 20 miles. A huge chunk appears to include Lake Washington blvd north of I-90 through the arboretum, which is a popular cycling route. Quite refreshing as it is in it's current state.
"Most of Seattle's Olmsted parks and connecting boulevards were built by 1908. The Olmsted plan incorporated previous proposals such as the ambitious 1892 ideas of City Parks Superintendent E. O. Schwagerl and the 1890s bicycle trails of City Engineer (later mayor) George Cotterill."