SOLUTION: An Airplane flew for 4 hours against headwind of 40 km/h. On the return flight the same wind was now a tail wind, and the flight took 3 hours. Find the speed of the airplane in

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: An Airplane flew for 4 hours against headwind of 40 km/h. On the return flight the same wind was now a tail wind, and the flight took 3 hours. Find the speed of the airplane in      Log On


   



Question 186418: An Airplane flew for 4 hours against headwind of 40 km/h. On the
return flight the same wind was now a tail wind, and the flight took 3
hours. Find the speed of the airplane in still air

Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
An Airplane flew for 4 hours against headwind of 40 km/h. On the
return flight the same wind was now a tail wind, and the flight took 3
hours. Find the speed of the airplane in still air
-------------
Downwind DATA:
rate = (p+40) km/h ; time = 3 hrs ; distance = rt = 3(p+40) km
------------------------
Upwind DATA:
rate = (p-40) km/h ; time = 4 hrs ; distance = rt = 4(p-40) km
-----------------------------
Equation:
distance = distance
3p+120 = 4p-160
p = 280 (speed of the plane in still air.
=============================================
Cheers,
Stan H.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let p = speed of plane in still air
Let d = distance travelled one way
given:
d+=+%28p+-+40%29%2A4 (against wind)
d+=+%28p+%2B+40%29%2A3 (with wind)
Since both are equal to d, set them
equal to eachother
%28p+-+40%29%2A4+=+%28p+%2B+40%29%2A3
4p+-+160+=+3p+%2B+120
p+=+280
The speed of plane in still air is 280 mi/hr
check:
d+=+%28p+-+40%29%2A4
d+=+%28p+%2B+40%29%2A3
-------------------
d+=+%28280+-+40%29%2A4
d+=+240%2A4
d+=+960
d+=+%28p+%2B+40%29%2A3
d+=+%28280+%2B+40%29%2A3
d+=+320%2A3
d+=+960
OK