Question

Driving to your friend's house, you travel at an average rate of 35 miles per hour. On your

home, you travel at an average rate of 40 miles per hour. If the round trip took you 45 minutes

how far is it from your house to your friend's house?

Answer 1

The distance from my house to friend's house is 14 miles

Explanation:

* Lets explain how to solve the problem

- Driving to the friend's house rate is 35 miles per hour

- Driving to my home rate is 40 miles per hour

- The round trip took 45 minutes

- We need to find the distance from my house to my friend's house

* At first lets change 45 minutes to hour because the rate of driving

unit is miles per hour

∵ 1 hour = 60 minutes

∴ 45 minutes =
`(45)/(60)=(3)/(4)` hour

- Assume that the distance from my house to friend's house is d,

the time for the trip from my house to the friend's house is
`t_(1)`

and the time from friend's house to my house is
`t_(2)`

∵ The distance between the two houses is d

∵ Distance = rate of driving × time of the trip

∴ d = 35 ×
`t_(1)` =
`35t_(1)`

∴ d = 40 ×
`t_(2)` =
`40t_(2)`

- Equate the two equations

∴
`35t_(1)` =
`40t_(2)`

- Divide both sides by 35

∴
`t_(1)=(40)/(35)t_(2)=(8)/(7)t_(2)`

∴
`t_(1)=(3)/(4)t_(2)` ⇒ (1)

- The time of the round trip is
`(3)/(4)` hour

∴
`t_(1)+t_(2)=(3)/(4)` ⇒ (2)

- Substitute equation (1) in equation (2)

∴
`(8)/(7)t_(2)+t_(2)=(3)/(4)`

∴
`(15)/(7)t_(2)=(3)/(4)`

- Divide Both sides by
`(15)/(7)`

∴
`t_(2)=0.35` hour

∵ d =
`40t_(2)`

- Substitute the value of
`t_(2)` in the equation above

∴ d = 40(0.35) = 14

∵ d represents the distance from my house to friend's house

∴ The distance from my house to friend's house is 14 miles

Answer 2

14 miles.

Explanation:

Let the distance traveled from home to destination = x miles.

Speed while going to friend's house = 35 miles per hour.

Speed while coming back = 40 miles per hour.

Total Time taken for the journey = 45 minutes = 0.75 hours.

Let the time taken while going to friend's house = y hours.

Therefore, the time taken while going to friend's house = (0.75 - y) hours.

To find x and y, model the speeds of both the journeys.

Speed while going to friend's house = Distance/Time.

35 = x/y.

x = 35y (Equation 1).

Speed while coming back = Distance/Time.

40 = x/(0.75 - y).

x = 40(0.75 - y) (Equation 2).

Since x = x, therefore:

35y = 30 - 40y.

75y = 30.

y = 30/75.

y = 0.4 hours.

Put y = 0.4 hours in Equation 1:

x = 35y.

x = 35(0.4).

x = 14.

Therefore, the distance between my friend's house and my house is 14 miles!!!