Question 188346
Let x= the  speed of Charlotte travel 
Let y= the  speed of Lorraine  travel
We can establish equations as follows:

(250/x) - 1 = 180/y ......(1)

x - 5     = y ..........(2)

(1) can be written : (250/x) -1 = 180/(x - 5)


or               (250 - x)/x = 180/(x-5)
               (250-x)(x-5)  = 180x
              250x-1250-x^2+5x = 180x
             -x^2+250x+5x-180x-1250 = 0
             x^2-75x+1250 = 0
x1 =[75+sqrt(75^2-4(1250)]/2= [75+ sqrt(625)]/2= 50
x2= [75-sqrt(625)]/2=25

two solutions if x=50 miles/hour then y= 45 miles/hour
                 x=25 miles /hour then y=20 miles/hour