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Flying to Tahiti with a tailwind a plane averaged 259 km/h. On the return trip the plane only
averaged 211 km/h while flying back into the same wind. Find the speed of the wind and the
speed of the plane in still air.

Respuesta :

mhanifa

Answer:

  • 235 km/h and 24 km/h

Step-by-step explanation:

Let the speed of the plane in sill air is p and the speed of the wind is w.

We have the following equations:

  • p + w = 259
  • p - w = 211

Add up the equations and solve for p:

  • 2p = 259 + 211
  • 2p = 470
  • p = 235

Find the value of w:

  • 235 + w = 259
  • w = 259 - 235
  • w = 24
Starrysoul100

[tex]\bold{\huge{\underline{ Solution }}}[/tex]

Given :-

  • Flying to Tahiti with a tailwind a plane averaged speed is 259km/h
  • On return trip, The plane only averaged 211km/h with the same wind

To Find :-

  • We have to find the speed of the wind and the speed of the plane in still air

Let's Begin :-

Let assume that the speed of plane is x

whereas, The speed of the wind is y

According to the first condition

  • Flying to Tahiti with a tailwind a plane averaged speed is 259 km/h

That is,

Speed of plane + Speed of wind = 259 km/h

Subsitute the required variables,

[tex]\bold{ x + y = 259 }[/tex]

[tex]\sf{ x = 259 - y...eq(1) }[/tex]

According to the second condition

  • On the return trip, The plane only averaged speed is 211 km/h with the air

That is,

Speed of plane - Speed of wind = 211 km/h

[tex]\bold{ x - y = 211 ...eq(2) }[/tex]

Subsitute eq(1) in eq( 2 ) :-

[tex]\sf{ 259 - y - y = 211 }[/tex]

[tex]\sf{ 259 - 2y = 211 }[/tex]

[tex]\sf{ - 2y = 211 - 259 }[/tex]

[tex]\sf{ - 2y = -48 }[/tex]

[tex]\sf{ y = }{\sf{\dfrac{-48}{-2}}}[/tex]

[tex]\sf{ y = }{\sf{\cancel{\dfrac{-48}{-2}}}}[/tex]

[tex]\bold{ y = 24 }[/tex]

Thus, The speed of wind that is y is 24 km/h

Now,

Subsitute the value of y in eq(1) :-

[tex]\sf{ x = 259 - 24 }[/tex]

[tex]\bold{ x = 235 }[/tex]

Hence, The speed of the wind and the plane in still is air are 24km/h and 235km/h .

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