Terrence walks at a pace of 2mi/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?

The answer to your question is the theater is 6.7 mi from home

Step-by-step explanation:

Data

speed 1 = 2 mi/h

time in theater = 2h 15 min

speed 2 = 40 mi/h

time = 3.5 h

Process

1. - Write the formula to calculate speed

speed = distance / time

-Solve for time

time = speed x time

2. - Write and equation to solve this problem

total time = time from home to theater + time from theater to home

3. - Substitution

3.5 = d/2 + d/40

4. - Solve for d

3.5 = (20d + d) / 40

140 = 21d

d = 140 / 21

d = 6.7 mi