Required information

Sometimes equations can be developed and practical problems solved by knowing nothing more than the dimensions of

the key parameters. For example, consider the heat loss through a window in a building. Window efficiency is rated in

terms of $R$ value, which has the unit of $f{t}^2*$ hr$.\frac{F}{?}$ Btu. A certain manufacturer offers a double$-$pane window with $R=2\mathrm{.}5$ and

also a triple$-$pane window with $R=3\mathrm{.}4.$ Both windows are $8$ ft by $6\mathrm{.}75$ ft $.$ On a given winter day, the temperature difference

between the inside and outside is $45F.$

Assume that a homeowner buys $20$ such triple$-$pane windows for the house. A typical winter equals about $120$ heating days at $T=$

$45$ F$.$ Each triple$-$pane window costs $$85$ more than a double$-$pane window. Ignoring interest and inflation, how many years will it take

the homeowner to make up the additional cost of the triple$-$pane windows from heating bill savings?

years