Answer:
The distance between the two parallel lines is 11/17 units
Explanation:
we have
8x-15y+5=0 -----> equation A
16x-30y-12=0 ----> equation B
Divide by 2 both sides equation B
8x-15y-6=0 ----> equation C
Compare equation A and equation C
Line A and Line C are parallel lines with different y-intercept
step 1
Find the slope of the parallel lines (The slope of two parallel lines is the same)
8x-15y+5=0
15y=8x+5

the slope is

step 2
Find the slope of a line perpendicular to the given lines
Remember that
If two lines are perpendicular then their slopes are opposite reciprocal (the product of their slopes is -1)

we have

therefore

step 3
Find the equation of the line perpendicular to the given lines
assume any point that lie on line A

For


To find the equation of the line we have
---> is the y-intercept

The equation in slope intercept form is
-----> equation D
step 4
Find the intersection point of the perpendicular line with the Line C
we have the system of equations
----> equation D
---->
----> equation E
equate equation D and equation E and solve for x

Multiply by 120 both sides to remove fractions



Find the value of y


the intersection point is

step 5
Find the distance between the points
and

the formula to calculate the distance between two points is equal to
substitute the values



Simplify

therefore
The distance between the two parallel lines is 11/17 units
see the attached figure to better understand the problem