Solution:
Let the distance of house from the theater be x miles.
Total travelling time[tex] =3.5-2.25=1.25 Hr [/tex]
Then average speed[tex] =\frac{Distance}{Time}= \frac{2x}{1.25}\\ [/tex]
Terrence walks at a pace of 2 mi/h to the theater and back home at 40 mi/h.
So Average Speed[tex] =\frac{2+40}{2}= 21\\ [/tex] mi/hr
Both the average speed should be equal. So we can write
[tex] \frac{2x}{1.25}=21\\ \\ 2x=1.25*21\\ \\ x=13.125\\ [/tex]
Hence the distance from home is 13.125 miles.
