Answer:
14 miles
Explanation:
The relation that will be used to solve this problem is:
[tex]Distance = Velocity*Time[/tex]
which can be rewritten as:
[tex]Time = \frac{Distance}{Velocity}[/tex]
Assume that:
Distance from your house to your friend's house is d
Time taken from your house to your friend's house is t₁
Time taken from your friends house to your house is t₂
1- From your house to your friend's house:
Average rate = 35 miles/hour
Therefore:
[tex]t_{1} = \frac{d}{35}[/tex]
2- From your friend's house to your house:
Average rate = 40 miles per hour
Therefore:
[tex]t_{2} = \frac{d}{40}[/tex]
3- Round trip:
We know that the round trip took 45 minutes which is equivalent to 0.75 hours
This means that:
t₁ + t₂ = 0.75 hours
[tex]\frac{d}{35}+\frac{d}{40}=0.75\\ \\\frac{40d + 35d}{1400}=0.75\\ \\\frac{75d}{1400}=0.75\\ \\ 1050 = 75d\\ d=14 miles[/tex]
Hope this helps :)
