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In a city 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. How far apart are the police station and the fire station?

User Ron Dadon
by
8.2k points

1 Answer

5 votes

Answer:

The distance between the police station and the fire station is 4 miles

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

User Paulo Bu
by
8.3k points

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