Carpenter's Question

Geometry Level 4

The part of the roof to the right of the valley has a 4-in-12 pitch, while the part to the left has a 3-in-12 pitch. A standard 8 by 4 sheet of plywood needs to be pre-cut on the ground before putting it on the right side, next to the gully, horizontally. If the cut starts in the corner, how far in along the longer side will it need to go? Round the answer to the nearest quarter of an inch. If it is \(a\) inches and \(b\) quarters of an inch, report \(a+b\).

Note: 4-in-12 pitch means that for every 12 horizontal inches the roof rises 4 vertical inches.

Clarification: \(b\) can only take the value of \(0,1,2\) or \(3\) only.

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