How far along this route is Terrence’s house from the theater?

Question

Terrence walks at a pace of 2 mi/h to the theater and watches 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 this route is Terrence’s house from the theater? Explain

Answer 1

Let V1 is the speed of 2 mi/h as Terrence walks to the theatre. So it is V1 = 2 mi/h

Let V2 is the speed as he comes back to his house from the theatre. It is V2 = 40 mi/h

It is V2 = 20 V1

if he walks for T1 hours to the theatre, he covers a distance of V1 * T1 = 2T1 miles

on his way back he covers the same distance  V2 * T2 = 40T2 miles (T2 is the time needed for the way back)

since the distance is the same it is  2T1 = 40T2  ==>>>  T1 = 20T2

the real travelling time is 3.5 - 2.15 = 1.35 hours so it is T1 + T2 = 1.35 hours we substitute where T1=20T2

and we get 21T2 = 1.35 hours so T2 = 1.35/21 = 0.0643 hours approx and T1 = 20T2 = 20 * 0.0643 ==>>>

T1 = 1.286 hours so the distance from his house to the theatre is 1.286 * 2 = 2.572 miles approx

the same as 0.0643 * 40 = 2.572 miles approx