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?

Question

Giana Raymond

Mathematics

11 November, 20:42

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?

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Answers (1)

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Paxton Cameron · Answer 1

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