Question

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

Answer 1

Answer:

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

Step-by-step 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 = $\frac{45}{60}=\frac{3}{4}$ 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

∴ $t_{1}=\frac{40}{35}t_{2}=\frac{8}{7}t_{2}$

∴ $t_{1}=\frac{3}{4}t_{2}$ ⇒ (1)

- The time of the round trip is $\frac{3}{4}$ hour

∴ $t_{1}+t_{2}=\frac{3}{4}$ ⇒ (2)

- Substitute equation (1) in equation (2)

∴ $\frac{8}{7}t_{2}+t_{2}=\frac{3}{4}$

∴ $\frac{15}{7}t_{2}=\frac{3}{4}$

- Divide Both sides by $\frac{15}{7}$

∴ $t_{2}=0.35$ 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

Answer:

14 miles.

Step-by-step 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!!!