Question 647961
The time they travel to reach this point is the same, and D=rt is the formula for distance, rate and time.  Divide both sides by r to find t=D/r<P>
In K's case she will travel some distance, x (D=x, a variable we don't know), so the t = x/32.  <P>
In Steve's case he'll travel 825-x (the full distance, minus whatever K travels, which is where they will meet.  For example if Karen travels 100 miles, then Steve must travel 825-100 = 725 miles to meet her.)  The same t, the time they travel to meet, is t= (825-x)/36.  <P>
Those two times are equal, so set the equations = to each other and solve for x.<P>
x/32 = (825-x)/36  Cross Multiply  36x = 26400 - 32x<P>
Bring the x's to the left...68x = 26400  Divide by 68  and x=388.24.<P>
Karen travels 388.24 miles before they meet.<P>