4 The time, \(X\) hours, taken by a large number of runners to complete a race is modelled by the probability density function given by $$f ( x ) = \begin{cases} \frac { k } { ( x + 1 ) ^ { 2 } } & 0 \leqslant x \leqslant a
0 & \text { otherwise } \end{cases}$$ where \(k\) and \(a\) are constants.

1. Show that \(k = \frac { a + 1 } { a }\).
2. State what the constant \(a\) represents in this context.
   Three quarters of the runners take half an hour or less to complete the race.
3. Find the value of \(a\).