SOLUTION: A plane flew 500km from Atlanta, GA to Louisville, KY. When returning to Atlanta, the flight took 1/2 hour less time. If the rate to Louisville was 60km/hr slower than the rate r

Question 243711: A plane flew 500km from Atlanta, GA to Louisville, KY. When returning to Atlanta, the flight took 1/2 hour less time. If the rate to Louisville was 60km/hr slower than the rate returning, find the two rates in km/hr.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A plane flew 500km from Atlanta, GA to Louisville, KY.
When returning to Atlanta, the flight took 1/2 hour less time.
If the rate to Louisville was 60km/hr slower than the rate returning, find the two rates in km/hr.
-----------------------------
GA to Louisville DATA:
distance = 500 km ; rate = x-60 km/hr ; time = d/r = 500/(x-60) hrs
------------------------------
Louisville to GA DATA:
distance = 500 km ; rate = x km/hr ; time = d/r = 500/x hrs
--------------------------------
Equation:
time to Louisville - time to GA = 1/2 hr
500/(x-60) - 500/x = 1/2
Multiply thru by 2x(x-60) to get:
1000x - 1000(x-60) = x(x-60)
60000 = x^2-60x
x^2-60x-60000 = 0
x = [60 +- sqrt(3600 - 4*-60000)]/2
Positive solution:
x = [60 + sqrt(243600)]/2
x = [60 + 493.56]/2
x = 276.78 km/hr (rate from Louisville to GA)
----------------
x-60 = 216.78 km/hr (rate from GA to Louisville)
============================
Cheers,
Stan H.
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