SOLUTION: Science and medicine. 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 takes 10 h, what is the plane's speed
Question 79596: Science and medicine. 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 takes 10 h, what is the plane's speed in still air? Answer by ptaylor(2198) (Show Source):
You can put this solution on YOUR website!
Distance(d) equals rate(r) times time(t) or d=rt; t=d/r and r=d/t
Let r=plane's speed in still air
Now we are told that time traveled against the wind plus time traveled with the wind equals 10h
Time traveled against the wind=720/(r-30)
Time traveled with the wind=720/(r+30)
So:
720/(r-30)+720/(r+30)=10 Multiply each term by (r+30)(r-30) to get rid of fractions
720(r+30)+720(r-30)=10(r+30)(r-30) simplify
720r+30(720)+720r-30(720)=10(r^2-900) or
1440r=10r^2-9000 subtract 1440r from both sides and divide both sides by 10:
r^2-144r-900=0 quadratic in standard form and this can be factored:
(r-150)(r+6)=0
r=150 mph-------------------------------------answer
and
r=-6 mph---------------discount negative speeds
CK
720/(150-30)+720/(150+30)=10
720/120+720/180=10
6+4=10
10=10
