Answer:
The distance between the police station and the fire station is 4 miles
Step-by-step explanation:
* Lets study the situation in the problem to solve it
- In the city there are three places, library , police station and fire station
- The distance between the library and the police station is 3 miles
less than twice the distance between the police station and the
fire station
- The distance between the library and the police station is 5 miles
* Lets change all of these situation to equations
# Let the distance between the library and the police station is x
# Let the distance between the police station and the fire station is y
∵ The distance between the library and the police station (x) is 3 miles
less than twice the distance between the police station and the
fire station (y)
∴ x = 2y - 3
∵ The distance between the library and the police station is (x) 5 miles
∴ x = 5
- Substitute the value of x in the equation above
∵ x = 2y - 3
∵ x = 5
∴ 5 = 2y - 3 ⇒ add 3 to both sides
∴ 8 = 2y ⇒ divide both sides by 2
∴ 4 = y
∵ y is the distance between the police station and the fire station
∴ The police station is 4 miles apart from the fire station
* The distance between the police station and the fire station is 4 miles
