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Gennadij [26K]
2 years ago
10

A plane can fly 540 miles with the wind in one hour less than it can fly 480 miles against the wind. The average wind speed is 3

0 miles per hour. Find the speed of the plane in still air.
Mathematics
1 answer:
Bess [88]2 years ago
3 0

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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