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.