SOLUTION: A family drove 1512 miles to their vacation lodge. Because of increased traffic density, their average speed on the return trip was decreased by 7 miles per hour and the trip took

Question 347354: A family drove 1512 miles to their vacation lodge. Because of increased traffic density, their average speed on the return trip was decreased by 7 miles per hour and the trip took 3 hours longer. Determine their original average speed on the way to the lodge.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A family drove 1512 miles to their vacation lodge. Because of increased traffic density, their average speed on the return trip was decreased by 7 miles per hour and the trip took 3 hours longer. Determine their original average speed on the way to the lodge.
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To lodge DATA:
rate = x mph ; distance = 1512 miles ; time = d/r = 1512/x hrs
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From lodge DATA:
rate = x-7 mph ; distance = 1512 miles ; time = 1512/(x-7) hrs
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Equation:
from time - to time = 3 hrs
1512/(x-7) -1512/x = 3
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1512x - 1512(x-7) = 3x(x-7)
---
1512*7 = 3x^2-21x
x^2 - 7x - 3528 = 0
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(x-63)(xx+56) = 0
Positive solution:
x = 63 mph (rate to the lodge)
x-7 = 56 mph (rate from the lodge)
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Cheers,
Stan H.
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