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At Maximum speed, an airplane travels 1680 miles against the wind in 5 hours. Flying with the wind, the plane can Travel the same distance in 4 hours.

Let x be the Maximum speed of the airplane and y be the speed of the wind. what is the speed of the plane with no wind?

Respuesta :

alinakincsem

Answer:

378 mph

Step-by-step explanation:

When the plane travels with the wind:

Distance = 1680 miles

Time = 4 hours

Rate = 1681 / 4 = 420 mph

When the plane travels against the wind:

Distance = 1680 miles

Time = 5 hours

Rate = 1681 / 5 = 336 mph

Given the above information, we can write the equations:

[tex]x+y=420[/tex]

[tex]x-y=336[/tex]

Adding these equations to get:

[tex]2x=756[/tex]

x = 378 mph

Therefore, 378 mph is the speed of the plane in still air.

luisejr77

Answer:

x = 378 miles/h

Step-by-step explanation:

First we calculate the module of both speeds.

With the wind against

[tex]s = \frac{distance}{time}[/tex]

s = d/t

d = 1680 miles

t = 5 hours

s = 1680/5

s = 336 miles/h

[tex]s = x -y[/tex] Because the wind speed goes in the direction opposite to that of the plane.

[tex]336 = x -y[/tex]

Flying with the wind.

s = 1680/4

s = 420

[tex]s = x + y[/tex] Because the wind speed goes in the same direction as the speed of the plane.

[tex]420 = x + y[/tex]

Now we have a system of 2 equations and 2 unknowns. We wish to find the value of x.

[tex]336 = x -y\\420 = x + y[/tex]

Resolving we have:

[tex]336 = x -y[/tex]

     +

[tex]420 = x + y[/tex]

-------------------------

[tex]756 = 2x[/tex]

x = 756/2

x = 378 miles/h

y = 42 miles/h

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