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It took a manticore the same amount of time to fly 10 miles with the wind as 5 miles against the wind. What is the speed of the speed of the wind if the manticore flies 30 mph in still air?

Respuesta :

Trancescient

Step-by-step explanation:

The time it takes for the manticore to travel 10 miles with the wind is given by

[tex]T_1 = \dfrac{10\:\text{mi}}{v_m + v_w}[/tex]

where [tex]v_m[/tex] is the speed of the manticore and [tex]v_w[/tex] is the speed of the wind.

Likewise, the time it takes for the manticore to travel 5 miles against the wind is

[tex]T_2 = \dfrac{5\:\text{mi}}{v_m - v_w}[/tex]

Since [tex]T_1 = T_2,[/tex] we can write

[tex]\dfrac{10\:\text{mi}}{v_m + v_w} = \dfrac{5\:\text{mi}}{v_m - v_w}[/tex]

After cross-multiplying,

[tex]10(v_m - v_w) = 5(v_m + v_w)[/tex]

[tex]\Rightarrow 10v_m - 10v_w = 5v_m + 5v_w[/tex]

Collecting similar terms, we get

[tex]15v_w = 5v_m[/tex]

Solving for [tex]v_w,[/tex] we get

[tex]v_w = \dfrac{5}{15}v_m = \dfrac{1}{3}v_m[/tex]

[tex]\:\:\:\:\:\:\:=\dfrac{1}{3}(30\:\text{mi/hr}) = 10\:\text{mi/hr}[/tex]

Speed of the wind as the mantle flies 30 mph is;

10 mph

  • We know that formula for time is;

t = distance/speed

Let v_m be speed of manticore

Let v_w be wind speed

  • Time for it to fly 10 miles with the wind is;

t = 10/(v_m + v_w)

  • Time for it to fly 5 miles against the wind is;

t = 5/(v_m - v_w)

I used negative sign between  v_m and v_w because the motion is against the wind.

  • Since we are told the mantle flies 30 mph in air and the times in both cases are equal, then we have;

10/(30 + v_w) = 5/(30 - v_w)

Rearranging gives us;

(10/5)(30 - v_w) = 30 + v_w

2(30 - v_w) = 30 + v_w

60 - 2v_w = 30 + v_w

30 = 3v_w

v_w = 30/3

v_w = 10 mph

Read more at; https://brainly.com/question/24897284

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