Respuesta :
It is given that the entire trip takes 3 and a half hours or in other words the entire trip takes 3.5 hours. Out of this, Terrance watches a movie for two hours and 15 minutes or 2.25 hours and that will have to be taken out of consideration and thus the nest time taken by Terrance is travelling from home to the theater on foot and then back in a bus is: [tex] 3.5-2.25=1.25 [/tex].
Now, let the distance between Terrance's home and theater be [tex] x [/tex].
Therefore, the time taken by Terrance to reach the theater on foot will be given by: [tex] \frac{x}{2}[/tex]
Likewise, the time taken by Terrance to reach his home in a bus that travels at a speed of 40 miles per hour will be given by: [tex] \frac{x}{40}[/tex]
Both will add up to make the total travel time of 1.25 hours. Thus, we will get the equation:
[tex] \frac{x}{2}+\frac{x}{40}=1.25[/tex]
This can be simplified as:
[tex] \frac{20x+x}{40}=1.25[/tex]
[tex] \frac{21x}{40}=1.25[/tex]
Multiplying both sides by 40 we will get:
[tex] 21x=40\times 1.25=50[/tex]
Dividing both sides by 21, we get:
[tex] x=\frac{50}{21}\approx2.381[/tex] miles
