Terrence walks at a pace of 2 mi/h to the theatre and watches a movie for 2h 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 3.5h , how far along this route is Terrence house from the theatre ? Explain.

The correct answer is: Terrence's house is approximately 2.38 miles away from the movie theatre

Step-by-step solution:-
Let the distance between Terrence's house and the movie theatre be x mi.
Total time taken = 3.5 hours
Total time taken = 3.5 × 60 minutes
Total time taken = 210 min .......................................................... (Equation i)
Now, we know that-
Time = Distance/speed
∴ Time taken while going to the theatre = Distance/ speed
∴ Time taken while going to the theatre = hours
∴ Time taken while going to the theatre = (×60 minutes .............................................. (1hour = 60 min)
∴ Time taken while going to the theatre = x × 30
∴ Time taken while going to the theatre = 30x min ...................................... (Equation ii)
Waiting time at Marta's house = 2 hours & 15 min
Waiting time at Marta's house = 2 60 minutes + 15 minutes ............................................. (1hour = 60 min)
Waiting time at Marta's house = 120 + 15 min
Waiting time at Marta's house = 135 min .............................................................. (Equation iii)
Time taken while coming back home = Distance/Speed
∴ Time taken while coming back home =  hours
∴ Time taken while coming back home = ()  60 minutes ........................ (1hour = 60 min)
∴ Time taken while coming back home = 1.5x min ........................................................ (Equation iv)
Total time taken = Time taken while biking to Marta's house + waiting time + Time taken while walking back home
∴ 210 = 30x + 135 + 1.5x ......................................................................... (From Equations i, ii, iii & iv)
∴ 210 = 31.5x + 135
∴ 210 - 135 = 31.5x ......................................................................................... (Taking all constants together)
∴ 75 = 31.5x
∴ 75/31.5 = x ............................................ (Dividing both sides by 31.5)
i.e. x = 75/31.5 or 2.38 miles
Final Answer:-
∴ Terrence's house is approximately 2.38 miles away from the movie theatre.