Question

In a city the distance between the libary and the police station is 3 miles less than than the distance between the police station and fire station the distance between the libary and police station is 5 miles how far apart are the police station and the fire station

Answer 1

8 miles

Explanation:

Given

Represent the police station with P, Library with L; Fire station with F

The first statement can be represented as:

`L - P = P - F - 3`

The second can be represented as:

`L - P = 5`

Required

Determine the distance between the police station and the fire station (P - F)

`L - P = P - F - 3` --- (1)

`L - P = 5` --- (2)

Substitute 5 for L - P in (1)

`5 = P - F - 3`

Add 3 to both sides

`3 +5 = P - F - 3 + 3`

`3 +5 = P - F`

`8= P - F`

`P - F = 8`