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!!!
The speed of the plane in still air is 150 miles per hour.
Speed is the ratio of distance travelled to total time taken. It is given by:
Speed = distance / time
Let a represent the speed of the plane and b represent the time taken when travelling with the wind.
Hence:
b = (540/(a+30)) + 1
Also:
(a - 30)b = 480
b = 480/(a - 30)
(540/(a+30)) + 1 = 480/(a - 30)
a = 150
The speed of the plane in still air is 150 miles per hour.
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