$5.$ The second floor $($i$.$e$.$ the actual floor between the lower level and the second level$)$ of a house consists of $$ inch thick plywood covered with $$ inch linoleum. Wool carpet, $(1)/(2)$ inch thick, is then installed over the linoleum. The temperature at the lower surface of the plywood is $75$oF$.$ The heat flow upwards through the floor is $5$ BTU$/$hr$.$ft$2.$ Determine the temperatures at the interfaces between each material and the temperature at the surface of the carpet, assuming ideal flat interfaces exist. Calculate the breakdown of the total resistance to heat transfer between materials. Use the following k values.