janet and lynn live 8 miles apart in opposite directions from their office. if lynn lives 1 mile less than twice as far from the office as janet does, how far does each live from the office?

x = Janet's distance to office

2x - 1 = Lynn's distance to office

x + 2x - 1 = 8
3x = 9
x = 3

x = 3 mi from Janet's house to office
2x - 1 = 5 miles Lynn's house to office

To solve this problem, we can set up a system of equations. Let's say Janet lives x miles from the office, and Lynn lives y miles from the office.

We know that they live 8 miles apart, which means the sum of their distances from the office is 8 miles:

x + y = 8 (Equation 1)

We also know that Lynn lives 1 mile less than twice as far from the office as Janet does. In equation form, this can be written as:

y = 2x - 1 (Equation 2)

Now, we can solve this system of equations by substituting Equation 2 into Equation 1:

x + (2x - 1) = 8

Simplifying this equation, we have:

3x - 1 = 8

Adding 1 to both sides, we get:

3x = 9

Dividing both sides by 3:

x = 3

Now that we have the value of x, we can substitute it back into Equation 2 to find y:

y = 2(3) - 1
y = 6 - 1
y = 5

Therefore, Janet lives 3 miles from the office, and Lynn lives 5 miles from the office.