SOLUTION: a plane flew 500 km from atlanta to louisville. when returning to atlanta the flight took 1/2 hour less time.if the rate to Louisville was 50km/hr faster than the rate returning, f

Question 299160: a plane flew 500 km from atlanta to louisville. when returning to atlanta the flight took 1/2 hour less time.if the rate to Louisville was 50km/hr faster than the rate returning, find the two rates in km/hr.
Found 2 solutions by mananth, MathTherapy:
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
a plane flew 500 km from atlanta to louisville. when returning to atlanta the flight took 1/2 hour less time.if the rate to Louisville was 50km/hr faster than the rate returning, find the two rates in km/hr.
let the returning rate be x kmh
time taken while returning = 500/x
the rate to louisville will be x+50 mph
the time taken while going is 500/ x+50
the distance traveled each way is 500 km
500/x -500/ x+50 = 1/2
500(x+50) - 500x= 1/2 * x(x+50)
500x+25000 -500x = x^2 +50x /2
2*500x +2 * 25000 = x^2 +50x
1000x +50000 = x^2 +50x
x^2-950x -50000=0
x^2-1000x+50x-50000=0
x(x-1000)+50(x-1000)=0
(x-1000)(x+50)=0
x=1000 km / hour returning rate
1050 km / hr is the going rate to louisville

Answer by MathTherapy(10556) (Show Source): You can put this solution on YOUR website!
a plane flew 500 km from atlanta to louisville. when returning to atlanta the flight took 1/2 hour less time.if the rate to Louisville was 50km/hr faster than the rate returning, find the two rates in km/hr.

This doesn't make sense!!

How can the return trip take less time than the outgoing one when the plane is traveling at a slower rate of speed on the return trip? This is not practical!!

It has to be that for the plane to take less time on the return trip, it has to be traveling at a faster rate of speed than it did on the outgoing trip to Louisville, not a slower one.
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