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For a romantic dinner, a couple took a small airplane for a quick flight to the countryside and then returned home. The plane flew a total of 5 hours, and each way the trip was 300 miles. If the plane was flying at 125mph, what was the speed of the wind that affected the plane?

Respuesta :

Answer:

25 mph

Explanation:

[tex]V_a[/tex] = Speed of airplane = 125 mph

[tex]V_w[/tex] = Speed of wind

Speed of plane moving against wind

[tex]V_a-V_w[/tex]

Speed of plane moving with wind

[tex]V_a+V_w[/tex]

Time taken to fly against wind

[tex]\frac{300}{V_a-V_w}[/tex]

Time taken to fly with wind

[tex]\frac{300}{V_a+V_w}[/tex]

Total time taken to fly both ways = 5 hours

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

So,

[tex]\frac{300}{V_a-V_w}+\frac{300}{V_a+V_w}=5\\\Rightarrow \frac{300(V_a+V_w+V_a-V_w)}{V_a^2-V_w^2}=5\\\Rightarrow \frac{300(2V_a}{V_a^2-V_w^2}=5\\\Rightarrow \frac{600V_a}{5}=V_a^2-V_w^2\\\Rightarrow 120V_a-V_a^2=-V_w^2\\\Rightarrow 120\times 125-125^2=-V_w^2\\\Rightarrow 15000-15625=-V_w^2\\\Rightarrow -625=-V_w^2\\\Rightarrow 625=V_w^2\\\Rightarrow V_w=25\ mph[/tex]

∴ Speed of wind is 25 mph

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