Yan is somewhere between his home and the stadium. To get to the stadium, he can either walk directly to the stadium or walk home first and then ride his bicycle to the stadium. He rides 7 times as fast as he walks, and both choices require the same amount of time. What is the ratio of Yan's distance from his home to his distance from the stadium? Express your answer in the form \(\frac{k}{m}\), where \(\frac{k}{m}\) is in simplest form, and provide the value of k + m.

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