SOLUTION: Hello, I cannot figure out how to set up the equation to solve the following problem; A plane flew 500 km from Atlanta, GA, to Louisville, KY. When returning to Atlanta, the

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Question 681960: Hello,
I cannot figure out how to set up the equation to solve the following problem;
A plane flew 500 km from Atlanta, GA, to Louisville, KY. When returning to Atlanta, the
flight took ½ hour less time. If the rate to Louisville was 50 km/hr slower than the rate
returning, find the two rates in km/hr.
Thanks in advance,
John
Found 2 solutions by ankor@dixie-net.com, josmiceli:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A plane flew 500 km from Atlanta, GA, to Louisville, KY.
When returning to Atlanta, the flight took ½ hour less time.
If the rate to Louisville was 50 km/hr slower than the rate returning, find the two rates in km/hr.
:
s = speed to Louisville
then
s + 50 = speed back to Atlanta
:
Write a time equation; time = dist/speed:
:
To time - return time = 1/2 hr
500%2Fs - 500%2F%28%28s%2B50%29%29 = .5

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
You need an equation for each trip
let +t+ = time for GA to KY flight in hrs
+t+-+.5+ = time for KY to GA flight in hrs
Let +r+ = rate going from KY to GA in km/hr
+r+-+50+ = rate going from GA to KY in km/hr
---------------------------------
Equation for GA to KY:
(1) +500+=+%28+r+-+50+%29%2At+
Equation for KY to GA:
(2) +500+=+r%2A%28+t+-+.5+%29+
---------------------
(1) +500+=+r%2At+-+50t+
(1) +r%2At+=+500+%2B+50t+
(1) +r+=+500%2Ft+%2B+50+
Substitute (1) into (2)
(2) +500+=+r%2A%28+t+-+.5+%29+
(2) +500+=+%28+500%2Ft+%2B+50+%29%2A%28+t+-+.5+%29+
(2) +500+=+500+%2B+50t+-+250%2Ft+-+25+
(2) +250%2Ft+=+50t+-+25+
(2) +250+=+50t%5E2+-+25t+
(2) +2t%5E2+-+t+-+10+=+0+
Use quadratic formula
+t+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+2+
+b+=+-1+
+c+=+-10+
+t+=+%28-%28-1%29+%2B-+sqrt%28+%28-1%29%5E2+-+4%2A2%2A%28-10%29+%29%29+%2F+%282%2A2%29+
+t+=+%28+1+%2B-+sqrt%28+1+%2B+80+%29%29+%2F+4+
+t+=+%28+1+%2B+9+%29+%2F+4+
+t+=+5%2F2+
and
(1) +r+=+500%2Ft+%2B+50+
(1) +r+=+500%2F%285%2F2%29+%2B+50+
(1) +r+=+200+%2B+50+
(1) +r+=+250+
and
+r+-+50+=+250+-+50+
+r+-+50+=+200+
The rate from GA to KY is 200 km/hr
The rate from KY to GA is 250 km/hr