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!!!
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 = [tex]\frac{45}{60}=\frac{3}{4}[/tex] 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 [tex]t_{1}[/tex]
and the time from friend's house to my house is [tex]t_{2}[/tex]
∵ The distance between the two houses is d
∵ Distance = rate of driving × time of the trip
∴ d = 35 × [tex]t_{1}[/tex] = [tex]35t_{1}[/tex]
∴ d = 40 × [tex]t_{2}[/tex] = [tex]40t_{2}[/tex]
- Equate the two equations
∴ [tex]35t_{1}[/tex] = [tex]40t_{2}[/tex]
- Divide both sides by 35
∴ [tex]t_{1}=\frac{40}{35}t_{2}=\frac{8}{7}t_{2}[/tex]
∴ [tex]t_{1}=\frac{3}{4}t_{2}[/tex] ⇒ (1)
- The time of the round trip is [tex]\frac{3}{4}[/tex] hour
∴ [tex]t_{1}+t_{2}=\frac{3}{4}[/tex] ⇒ (2)
- Substitute equation (1) in equation (2)
∴ [tex]\frac{8}{7}t_{2}+t_{2}=\frac{3}{4}[/tex]
∴ [tex]\frac{15}{7}t_{2}=\frac{3}{4}[/tex]
- Divide Both sides by [tex]\frac{15}{7}[/tex]
∴ [tex]t_{2}=0.35[/tex] hour
∵ d = [tex]40t_{2}[/tex]
- Substitute the value of [tex]t_{2}[/tex] 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
