# SOLUTION: A family drove 1080 miles to their vacation lodge. Because of increased traffic density, their average speed on the return trip was decreased by 6 miles per hour and the trip took

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 Question 606583: A family drove 1080 miles to their vacation lodge. Because of increased traffic density, their average speed on the return trip was decreased by 6 miles per hour and the trip took 2 1/2 hours longer. Determine their average speed on the way to the lodge.Answer by LisaJ(11)   (Show Source): You can put this solution on YOUR website!Define some variables: Speed going to lodge = V1 mph Travel time = T1 hours Speed going home = (V1 - 6) mph Time going home = (T1 + 2.5) hours Distance = speed * time = 1080 miles equation 1: V1 * T1 = 1080 equation 2: (V1 - 6) * (T1 + 2.5) = 1080 Solve for V1 and T1: From eq 1, T1 = 1080/V1 substitute this into eq 2: (V1 - 6) * [(1080/v1) + 2.5] = 1080 Simplify this to get a quadratic for V1: Solve; v1 = 54 or -48. Only a positive answer makes sense. V1 = 54 mph Check: T1 = 1080/54 = 20 hours. V2 = V1 - 6 = 48 mph T2 = 20 + 2.5 = 22.5 hours 48 mph * 22.5 hours = 1080 miles