Three planks of different lengths, X, Y and Z are nailed together to make a frame as shown. Plank X has 3 holes which divide it into 4 equal parts. Plank Y has 4 holes which divide it into 5 equal parts and Plank Z has 5 holes which divide it into 6 equal parts. In the frame, the holes R, S and T are three corners of an equilateral triangle. Plank X is 312 cm long. What is the total length of Plank X, Plank Y and Plank Z?
Length of Plank X = 312 cm

Length of each interval of Plank X
= 312 ÷ 4
= 78 cm

Length of 2 intervals of Plank X
= 2 x 78
= 156 cm

Length of each interval of Plank Y 
= 156 ÷ 3
= 52 cm

Length of Plank Y
= 5 x 52
= 260 cm

Length of each interval of Plank Z
= 156 ÷ 4
= 39 cm

Length of Plank Z
= 6 x 39
= 234 cm

Total length of Plank X, Plank Y and Plank Z
= 312 + 260 + 234
= 806 cm

Answer(s): 806 cm