Question

terrance walks at a pace of 2 mi/h to the Theater and watch the movie for two hours and 15 minutes. he ride back home taking the same route on the bus that travels at a rate of 40 mph. the entire trip takes 3 1/2 hours. how far along this route is Terrence’s house from theater

Answer 1

To find the distance between Terrence's house and the theater, we calculate the distance he walked and the distance he traveled on the bus. The total distance is 54.5 miles.

Step-by-step explanation:

To find the distance between Terrence's house and the theater, we need to calculate the total distance he traveled. We know that he walked at a pace of 2 mi/h to the theater and watched the movie for 2 hours and 15 minutes. This means he walked for a total of 2.25 hours (2 hours + 15 minutes converted to hours).

The distance he walked can be calculated using the formula Distance = Speed x Time. So, the distance he walked is 2.25 hours x 2 mi/h = 4.5 miles.

Next, we need to find the time it took for Terrence to ride back home on the bus. We know that the entire trip took 3.5 hours and he walked for 2.25 hours. So, the time he spent on the bus is 3.5 hours - 2.25 hours = 1.25 hours.

Using the formula Distance = Speed x Time, we can calculate the distance he traveled on the bus. The distance is 1.25 hours x 40 mi/h = 50 miles.

Therefore, the total distance between Terrence's house and the theater is the sum of the distances he walked and the distance he traveled on the bus. The total distance is 4.5 miles + 50 miles = 54.5 miles.

Answer 2

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:
`3.5-2.25=1.25`.

Now, let the distance between Terrance's home and theater be
`x`.

Therefore, the time taken by Terrance to reach the theater on foot will be given by:
`(x)/(2)`

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:
`(x)/(40)`

Both will add up to make the total travel time of 1.25 hours. Thus, we will get the equation:

`(x)/(2)+(x)/(40)=1.25`

This can be simplified as:

`(20x+x)/(40)=1.25`

`(21x)/(40)=1.25`

Multiplying both sides by 40 we will get:

`21x=40* 1.25=50`

Dividing both sides by 21, we get:

`x=(50)/(21)\approx2.381` miles