Terrence walks at a pace of 2 mi/h to the theater and watched a movie for 2 h and 15 min. He rides back home, taking the same route, on the bus that travels at a rate of 40 mi/h. The entire trip takes 3.5 h. How far along is this route is Terrence's house from the theater? Explain.

D = distance of Terrence's house from the theater

v₁ = speed at which Terrence walk from home to theater = 2 mi/h

t₁ = time taken by Terrence to walk from home to theater = D/v₁ = D/2

v₂ = speed at which Terrence returns back to home = 40 mi/h

t₂ = time taken by Terrence to return back to home = D/v₂ = D/40

t' = time spent in watching the movie = 2 h 15 min = 2.25 h

t = total time = 3.5 h

we know that

t = t₁ + t₂ + t'

3.5 = (D/2) + (D/40) + 2.25

D = 2.4 miles