Problem #$1)$ Calculating R$-$Values and U$-$Values of a wall assembly $(10$ Points$)$

We will be calculating the overall U$-$value for the above wall assembly by calculating R$-$values and Uvalues for individual layers and components, then adding complexity to those layers. The section of wall we are examining is ${40}^{\text{'}}$ wide by ${12}^{\text{'}}$ tall. The wall is constructed with $26$ wood framing, pink batt insulation, blue insulation, and exterior siding.

$1.$a$)$ Consider just the innermost layer of the wall consisting of pink batt insulation and wood framing.

The R$-$value for the insulation is for the entire thickness of the pink insulation between the $26$ framing is R$-24.$

Assume the layout of the $26s$ is ${24}^{27}$ on$-$center. The R$-$value for the $26$ is $1\mathrm{.}1$ per inch of wood thickness.

Calculate the aggregate U value for the combination of $26s$ and pink batt insulation. Calculate this to three decimal places.

$1.$b$)$ Calculate the R$-$value for the combination of $26s$ and pink batt insulation. Calculate this to two decimal places.