A geometry problem by Ossama Ismail

Geometry Level 3

There is a 24 m long row of students marching ahead. The last student in the row wants to give a flag to the first student in the row. So while the students are marching he runs ahead, reaches the first student and hands over the flag to him and without stopping he runs back to his original position. In the mean time the whole row has moved ahead by 24 m.
Assume the total distance covered by the last student is \(D\) and his speed is uniform.

\[ D = (1 + \sqrt 2 ) \times S \]

What is the value of \(S\)?


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