Answer:
The distance from my house to friend's house is 14 miles
Step-by-step explanation:
* <em>Lets explain how to solve the problem</em>
- 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
* <em>At first lets change 45 minutes to hour because the rate of driving</em>
<em> unit is miles per hour</em>
∵ 1 hour = 60 minutes
∴ 45 minutes =
hour
- <em>Assume that the distance from my house to friend's house is d,</em>
<em> the time for the trip from my house to the friend's house is</em>
<em>and the time from friend's house to my house is</em> 
∵ The distance between the two houses is d
∵ Distance = rate of driving × time of the trip
∴ d = 35 ×
= 
∴ d = 40 ×
= 
- <u><em>Equate the two equations</em></u>
∴
= 
- Divide both sides by 35
∴
∴
⇒ (1)
- The time of the round trip is
hour
∴
⇒ (2)
- <u><em>Substitute equation (1) in equation (2)</em></u>
∴ 
∴ 
- Divide Both sides by 
∴
hour
∵ d = 
- Substitute the value of
in the equation above
∴ d = 40(0.35) = 14
∵ <u><em>d represents the distance from my house to friend's house</em></u>
∴ The distance from my house to friend's house is 14 miles