SOLUTION: Flying against the wind, an airplane travels 5100 km in 6 hours. Flying with the wind, the same plane travels 5750 km in 5 hours. What is the rate of the plane in still air and wha

Question 799008: Flying against the wind, an airplane travels 5100 km in 6 hours. Flying with the wind, the same plane travels 5750 km in 5 hours. What is the rate of the plane in still air and what is the rate of the wind?
Answer by Finavon(81) (Show Source): You can put this solution on YOUR website!
Wind speed w; plane airspeed p
Dist=speed * time
with wind: (p+w)*5 = 5750 (1)
against: (p-w)*6 = 5100 (2)
(1) 5p+5w=5750
(2)+650: 650+6p-6w = 5100+650 = 5750 = (1)
so 5p+5w=650+6p-6w
11w=650+p or p=(11w-650) (3)
subst for p in (1): 5*(11w-650)+5w = 5750
55w+5w-3250 = 5750 or 60w = 9000
w=150
subst in (3): p=11*150 - 650 = 1650-650 = 1000
Plane 1000 km/hr; Wind 150 km/hr
Check:
with: 1150*5= 5750
against: 850*6= 5100
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