SOLUTION: A plane flies 720 mi against a steady 30 mi.h headwind and then returns to the same point with the wind. If the entire trip takes 10 hr what is the planes speed in still air?: A pl
Algebra.Com
Question 83265: A plane flies 720 mi against a steady 30 mi.h headwind and then returns to the same point with the wind. If the entire trip takes 10 hr what is the planes speed in still air?: A plane flies 720 mi against a steady 30 mi.h headwind and then returns to the same point with the wind. If the entire trip takes 10 hr what is the planes speed in still air?
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Let x=speed (rate) of the plane in still air
speed against headwind =x-30
speed with headwind=x+30
Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r
Time required travelling against the headwind=720/(x-30)
Time require travelling with the headwind=720/(x+30)
Now we are told that the total time was 10 hours, So:
720/(x-30)+720/(x+30)=10 multiply both sides by (x-30)(x+30)
720(x+30)+720(x-30)=10(x-30)(x+30) divide both sides by 10
72(x+30)+72(x-30)=(x-30)(x+30) get rid of parens
72x+2160+72x-2160=x^2-900 collect like terms
144x=x^2-900 subtract 144x from both sides
144x-144x=x^2-144x-900 simplify
x^2-144x-900=0 quadratic in standard form and this can be factored
(x-150)(x+6)=0
x=150mph-------------------------------------rate in still air
x=-6----------------discount negative value for speed
CK
720/(150-30)+720/(150+30)=10
6+4=10
10=10
Hope this helps---ptaylor
RELATED QUESTIONS
A plane flies 720 mi against a steady 30-mi/h headwind
and then returns to the same... (answered by checkley71,stanbon)
A plane flies 720 mi against a steady 30 mi/h headwind and then returns to the same point (answered by checkley75)
A plane flies 720 mi against a steady 30-mi/h headwind and then returns to the same point (answered by stanbon)
A plane flies 720 mi against a steady 30-mi/h headwind
and then returns to the same... (answered by checkley71)
A plane flies 720 mi against a steady 30-mi/h headwind and then returns to the same point (answered by stanbon,solver91311)
Science and medicine. A plane flies 720 mi against a steady 30 mi/h headwind and then... (answered by ptaylor)
a plane flies 720 mi against a steady 30 mi/h headwind and then returns to the same point (answered by Paul)
A plane flies 720 mi against a steady 30-mi/h headwind and then returns to the same point (answered by fractalier)
A plane flies 720 mi. against a steady 30-mi/h headwind and then returns to the same... (answered by fractalier)
A plane flies 720 mi against a steady 30-mi/h headwind and then returns to the same point (answered by checkley71)