SOLUTION: A plane flies 720 miles against a steady 30mi/h headwind and then returns to the same point with the wind. If the entire trip takes 10 hrs, what is the plane's speed in still

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: A plane flies 720 miles against a steady 30mi/h headwind and then returns to the same point with the wind. If the entire trip takes 10 hrs, what is the plane's speed in still       Log On


   

Question 115726:
A plane flies 720 miles against a steady 30mi/h headwind and then returns to the same point with the wind. If the entire trip takes 10 hrs, what is the plane's speed in still air?

720/30 = 10/x
720x = 30*10
720x = 300
720x/720 = 300/720
Am I on the right track on solving this problem because the answer I come up with is not a whole number?
Found 2 solutions by josmiceli, checkley71:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
s = the plane's speed in still air
w = wind speed
The problem says w+=+30 mi/hr
(time going) + (time returning) = total time
The problems says total time = 10 hrs
Note that distance/rate = time
720+%2F+%28s+-+w%29+%2B+720+%2F+%28s+%2B+w%29+=+10
720+%2F+%28s+-+30%29+%2B+720+%2F+%28s+%2B+30%29+=+10
multiply both sides by %28s+-+30%29%28s+%2B+30%29
720%28s+%2B+30%29+%2B+720%28s+-+30%29+=+10%28s+%2B+30%29%28s+-+30%29
720s+%2B+21600+%2B+720s+-+21600+=+10%28s%5E2+-+900%29
1440s+=+10s%5E2+-+9000
10s%5E2+-+1440s+-+9000+=+0
s%5E2+-+144s+-+900+=+0
solve using quadratic formula
s+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a = 1
b = -144
c = -900
s+=+%28-%28-144%29+%2B-+sqrt%28+%28-144%29%5E2-4%2A1%2A%28-900%29+%29%29%2F%282%2A1%29+
s+=+%28144+%2B-+sqrt%2820736+%2B+3600%29%29+%2F+2
s+=+%28144+%2B-+156%29+%2F+2
s+=+150
s+=+-6
The positive answer is the only one that makes sense
The plane's speed in still air is 150 mi/hr
check answer:
720+%2F+%28s+-+w%29+%2B+720+%2F+%28s+%2B+w%29+=+10
720+%2F+%28150+-+30%29+%2B+720+%2F+%28150+%2B+30%29+=+10
720+%2F+120+%2B+720+%2F+180+=+10
6+%2B+4+=+10
OK

Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
D=RT
T=D/R
10=720/(R-30)+720/(R+30) COMBINE THE FRACTIONS USING THE COMMON DENOMINATOR:
(R-30)(R+30)
10=[720(R+30)+720(R-30)]/(R-30)(R+30)
10=(720R+21600+720R-21600)/(R^2-900)
10=1440R/(R^2-900) CROSS MULTIPLY
10(R^2-900)=1440R
10R^2-1440R-9000=0
10(R^2-144R-900)=0
10(R-150)(R+6)=0
5-150=0
R=150 ANSWER FOR THE SPEED OF THE AIRPLANE.
PROOF
10=720/(150-30)+720/(150+30)
10=720/180+720/120
10=4+6
10=10