# 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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 Click here to see ALL problems on Travel Word Problems 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)   (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