Answer:
The speed of the plane in still air = 150 mph
Step-by-step explanation:
This is a relative velocity question
Let the velocity of the plane in still air be v
And let the time the plane can fly 480 miles against the wind be t
(Velocity of the plane relative to the wind) = (velocity of plane) - (velocity of wind)
Flying against the wind
(Velocity of plane relative to the wind) = (480/t)
(Velocity of the plane) = v
(Velocity of the wind) = 30 mph
(480/t) = v - 30
t = 480/(v-30) (eqn 1)
Flying with the wind
(Velocity of plane relative to the wind) = 540/(t-1)
(Velocity of the plane) = v
(Velocity of the wind) = -30 mph
540/(t - 1) = v + 30
t - 1 = 540/(v+30) (eqn 2)
Since t is equal in both cases, substitute the value of t in eqn 1 into eqn 2.
[480/(v-30)] - 1 = [540/(v+30)]
Multiply through by (v+30)(v-30)
480(v+30) - [(v+30)(v-30)] = 540(v-30)
480v + 14400 - (v² - 900) = 540v - 16200
480v + 14400 - v² + 900 = 540v - 16200
v² + 540v - 480v - 16200 - 14400 - 900 = 0
v² + 60v - 31500 = 0
Solving the quadratic equation,
v = 150 mph or v = -210 mph
We'll pick the positive answer because of the directions we have established.
Therefore, the speed of the plane in still air = 150 mph
Hope this Helps!!!
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