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A young Witch flew her broom 48 miles form her home to a witch festival. Flying with the wind, the trip took 3 hours. Her flight home against the wind took 4 fours. find the speed of the wind and the speed of the broom in still air

Respuesta :

Using the relation between velocity, distance and time, it is found that:

  • The speed of the wind is of 2 mph.
  • The speed of the broom is of 14 mph.

What is the relation between velocity, distance and time?


Velocity is distance divided by time, hence:

[tex]v = \frac{d}{t}[/tex]

Flying with the wind, in which [tex]v = v_b + v_w[/tex] the 48-mile trip took 3 hours, hence:

[tex]v = \frac{d}{t}[/tex]

[tex]v_b + v_w = \frac{48}{3}[/tex]

[tex]v_b + v_w = 16[/tex]

Her flight home against the wind took 4 fours, hence:

[tex]v = \frac{d}{t}[/tex]

[tex]v_b - v_w = \frac{48}{4}[/tex]

[tex]v_b - v_w = 12[/tex]

Adding the two equations:

[tex]2v_b = 28[/tex]

[tex]v_b = 14[/tex]

[tex]v_b + v_w = 16 \rightarrow v_w = 2[/tex]

Hence:

  • The speed of the wind is of 2 mph.
  • The speed of the broom is of 14 mph.

More can be learned about the relation between velocity, distance and time at https://brainly.com/question/24316569

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