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

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

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