SOLUTION: When a plane flies into the wind , it can travel 3000km in 6 hours. When it flies with the wind, it can travel the same distance in 5 hours. Find the rate of the plane in still air

Question 948147: When a plane flies into the wind , it can travel 3000km in 6 hours. When it flies with the wind, it can travel the same distance in 5 hours. Find the rate of the plane in still air and the rate of the wind.
I sorta know how to do these problems. I am just a little confused on this one. Could you help me with this one please?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
RT=D rate time distance

VARIABLES
r, speed if no wind
w, speed of wind
u, time in a direction of travel
v, time in the opposite direction of travel
d, distance one way or either way for the trip
-
u=6
v=5
d=3000
-
Unknown variables for which to solve are r and w.

Related to wind__________rate___________time___________distance
AGAINST__________________r-w______________u______________d
WITH_____________________r+w______________v______________d

System of equations before refinements:

Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!

When a plane flies into the wind , it can travel 3000km in 6 hours. When it flies with the wind, it can travel the same distance in 5 hours. Find the rate of the plane in still air and the rate of the wind.
I sorta know how to do these problems. I am just a little confused on this one. Could you help me with this one please?

Let speed of plane in still air, be S, and speed of wind, W
Average speed when flying against wind: , or 500 km
Average speed when flying with wind: , or 600 km
Speed of plane in still air, less wind�s speed, equals average speed against wind, OR
S � W = 500 -------- eq (i)
Speed of plane in still air, plus wind�s speed, equals average speed with wind, OR
S + W = 600 -------- eq (ii)
2S = 1,100 -------- Adding eqs (ii) & (i)
S, or speed of plane in still air = , or km/h
550 � W = 500 -------- Substituting 550 for S in eq (i)
- W = 500 � 550
- W = - 50
W, or speed of wind = , or km/h
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