A train accelerates uniformly from rest to a speed \(v\) m/s. It continues at this speed for a period of time and then decelerates uniformly to rest. In travelling a total distance \(d\) m the train accelerates through a distance \(pd\) m and decelerates through a distance \(qd\) m, where \(p < 1\) and \(q < 1\).

If the average speed of the train for the whole journey is \(\dfrac{v}{p+q+b}\), find \(b\).

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