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 x be the distance from home

The total time taken is 3.5 hours or 3 hours 30 mins

Out of which he had spend 2 hours 15 mins at the theatre

Hence the time taken by him in the travel to and from his home is

3 hours 30 mins - 2 hours 15 mins = 1 hour 15 mins or 1.25 hours

Lets calculate the time t₁ taken to walk from his home to the theatre

$time= \frac{distance}{speed}$

t₁ = $\frac{x}{2}$

now the time t₂ taken to travel from theater to home

t₂ = $\frac{x}{40}$

Now both of these time add up to 1.25 hours

$\frac{x}{2} +\frac{x}{40} = 1.25$

$\frac{20x}{40} +\frac{x}{40} =1.25$

$\frac{21x}{40} =1.25$

$x= 1.25 .\frac{40}{21}$

$x = 2.38$

Hence the distance from the home to the theater = 2.38 miles