SOLUTION: The speed of an airplane in still air is 214mph. The plane travels 819mi against the wind and 1505 mi with the wind in a total time of 12 hrs. what is the speed of the wind?
Algebra.Com
Question 65311: The speed of an airplane in still air is 214mph. The plane travels 819mi against the wind and 1505 mi with the wind in a total time of 12 hrs. what is the speed of the wind?
Found 2 solutions by checkley71, stanbon:
Answer by checkley71(8403) (Show Source): You can put this solution on YOUR website!
12=819/(214-X)+1505/(214+X)
12=[819(214+X)+1505(214-X)]/(214-X)(214+X)
12=(175266+819X+322070-1505X)/(45796-X^2)
12(45796-X^2)=-686X+497336
549552-12X^2+686X-497336=0
12X^2-686X-52216=0
USING THE QUADRATIC EQUATION WE GET X=100.4745 THE SPEED OF THE WIND
PROOF
12=819/(214-100.4745)+1505/(214+100.4745)
12=819/113.5255+1505/314.4745
12=7.2142382+4.7857616
12=12
#######################################################################
MERRY CHRISTMAS
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The speed of an airplane in still air is 214mph. The plane travels 819mi against the wind and 1505 mi with the wind in a total time of 12 hrs. what is the speed of the wind
---------
Let "w" be the speed of the wind.
------------
Against the wind DATA:
distance=819 miles ; Rate=(214-w); time= d/r=819/(214-w) hrs
-----------------------
With the wind DATA:
distance=1505 miles ; rate=(214+w); time = d/r 1505/(214+w) hrs
------------
EQUATION:
time + time = 12 hrs
819/(214-w) + 1505/(214+w) = 12
819(214+w) + 1505(214-w)= 12(214^2-w^2)
(2324)(214)+(819-1505)w = 12(45796)-12w^2
12w^2-686w-52216=0
6w^2-343w-26108=0
w=[343+-sqrt(343^2-4*6*-26108]/12
w=[1205.69]/12
w=100.47 mph (speed of the wind)
Cheers,
Stan H.
RELATED QUESTIONS
The speed of an airplane in still air is 243 mph. The plane travels 663 mi against the... (answered by ankor@dixie-net.com)
the speed of an airplane in still air is 257 mph. the plane travels 570 mi against the... (answered by stanbon)
The speed of an airplane in still air is 248 mph. The plane travels 816 mi agains the... (answered by josmiceli)
An airplane flies 738 mi against the wind and 1062 mi with the wind in a total time of 9... (answered by checkley77)
the speed of an airplane in still air is 224km/h. the plane travels 716 km against the... (answered by ptaylor)
THE SPEED OF AN AIRPLANE IN STILL AIR IS 224KM/H. THE PLANE TRAVELS 733KM AGAINST THE... (answered by solver91311,josmiceli,ankor@dixie-net.com)
Speed of an airplane in still air is 255 km/h. plane travels 675km against wind and 1449... (answered by ankor@dixie-net.com)
An airplane flies 1449 mi against the wind
and 1539 mi with the wind in a total time of... (answered by josmiceli)
the speed of an airplane in still air is 153 mph. The plane travels 849 mph against the... (answered by ptaylor)