SOLUTION: An airplane flying against the wind travels 500 miles in the same amount of time it would take the same plane to travel 600 miles with the wind. If the wind speed is a constant 50

Question 1055875: An airplane flying against the wind travels 500 miles in the same amount of time it would take the same plane to travel 600 miles with the wind. If the wind speed is a constant 50 miles per hour, how fast would the plane travel in still air?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
Constant Travel Rate Rule, RT=D

SPEED TIME DISTANCE AGAINST WIND r-50 t 500 WITH WIND r+50 t 600

Make the system of the two needed equations and solve for t and r.
Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!

An airplane flying against the wind travels 500 miles in the same amount of time it would take the same plane to travel 600 miles with the wind. If the wind speed is a constant 50 miles per hour, how fast would the plane travel in still air?

Let speed of plane in still air be S
Against the wind, time plane takes to travel 500 miles is:
With the wind, time plane takes to travel 600 miles is:
Since the times are identical, we get the following TIME equation:
600(S - 50) = 500(S + 50) ------- Cross-multiplying
6(S - 50) = 5(S + 50) ------- Dividing both sides by 100
6S - 300 = 5S + 250
6S - 5S = 250 + 300
S, or speed of plane in still air =
FYI: You DON'T NEED to find time to determine the speed of the plane in still air, regardless of what others might tell you, unless you want to.
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