Maths-

General

Easy

Question

# Terrence walks at a pace of 2 mi/h to the theatre and watches a movie for 2h 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 3.5h , how far along this route is Terrence house from the theatre ? Explain.

Hint:

### 1. Speed = Distance/time

2. Total time taken = time taken while going to the theatre + movie time + time taken while coming back home

## The correct answer is: Terrence's house is approximately 2.38 miles away from the movie theatre

### Step-by-step solution:-

Let the distance between Terrence's house and the movie theatre be x mi.

Total time taken = 3.5 hours

Total time taken = 3.5 × 60 minutes

Total time taken = 210 min .......................................................... (Equation i)

Now, we know that-

Time = Distance/speed

∴ Time taken while going to the theatre = Distance/ speed

∴ Time taken while going to the theatre = hours

∴ Time taken while going to the theatre = (×60 minutes .............................................. (1hour = 60 min)

∴ Time taken while going to the theatre = x × 30

∴ Time taken while going to the theatre = 30x min ...................................... (Equation ii)

Waiting time at Marta's house = 2 hours & 15 min

Waiting time at Marta's house = 2 60 minutes + 15 minutes ............................................. (1hour = 60 min)

Waiting time at Marta's house = 120 + 15 min

Waiting time at Marta's house = 135 min .............................................................. (Equation iii)

Time taken while coming back home = Distance/Speed

∴ Time taken while coming back home = hours

∴ Time taken while coming back home = () 60 minutes ........................ (1hour = 60 min)

∴ Time taken while coming back home = 1.5x min ........................................................ (Equation iv)

Total time taken = Time taken while biking to Marta's house + waiting time + Time taken while walking back home

∴ 210 = 30x + 135 + 1.5x ......................................................................... (From Equations i, ii, iii & iv)

∴ 210 = 31.5x + 135

∴ 210 - 135 = 31.5x ......................................................................................... (Taking all constants together)

∴ 75 = 31.5x

∴ 75/31.5 = x ............................................ (Dividing both sides by 31.5)

i.e. x = 75/31.5 or 2.38 miles

Final Answer:-

∴ Terrence's house is approximately 2.38 miles away from the movie theatre.

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