A uniform plank PQ of length 8m and mass 10kg is supported horizontally at the end P and at point R, 3 metres from Q. A boy of mass 20 kg walks along the plank starting from P. If the plank is in equilibrium, calculate the 

(a) reactions at P and R when he walked 1.5 metres;

(b) distance he had walked when the two reactions are equal;

(c) distance he walked before the plank tips over.