SOLUTION: Charlotte's time to travel 250 miles is 1 hour more than Lorraine's time to travel 180 miles. Charlotte drove 5 miles per hour faster than Lorraine. How fast did each one travel.

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Question 188346This question is from textbook
: Charlotte's time to travel 250 miles is 1 hour more than Lorraine's time to travel 180 miles. Charlotte drove 5 miles per hour faster than Lorraine. How fast did each one travel.
thanks,
I know this problem involves the quadratic equation and I know there will be two different possible scenarios. I just need help seting up the equation. This question is from textbook

Answer by dukesmart(20) About Me  (Show Source):
You can put this solution on YOUR website!
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