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Sagot :
Answer:
The speed of the plane = 412 miles per hour
The speed of the wind = 18 miles per hour.
Explanation:
Let's call x the speed of the plane and y the speed of the wind.
Then, the distance that a plane traveled can be calculated as:
[tex]d=v\cdot t[/tex]Where v is the sum of the speed of the plane and the speed of the wind and t is the number of hours.
Now, if the plane traveled 1290 miles with the wind (downwind) for 3 hours, we can write the following equation:
[tex]1290=(x+y)\cdot3^{}[/tex]In the same way, if the plane traveled 1576 miles against the wind (upwind) for 4 hours, we get:
[tex]1576=(x-y)\cdot4[/tex]So, the systems of equations is equal to:
1290 = 3(x + y)
1576 = 4(x - y)
Solving for x in the first equation, we get:
[tex]\begin{gathered} \frac{1290}{3}=\frac{3(x+y)}{3} \\ 430=x+y \\ 430-y=x+y-y \\ 430-y=x \end{gathered}[/tex]Now, we can substitute x = 430 - y on the second equation and solve for y:
[tex]\begin{gathered} 1576=4((430-y)-y_{}) \\ 1576=4(430-2y) \\ \frac{1576}{4}=\frac{4(430-2y)}{4} \\ 394=430-2y \\ 394-430=430-2y-430 \\ -36=-2y \\ \frac{-36}{-2}=\frac{-2y}{-2} \\ 18=y \end{gathered}[/tex]Finally, we can calculate the value of x:
[tex]\begin{gathered} x=430-y \\ x=430-18 \\ x=412 \end{gathered}[/tex]Therefore, the speed of the plane is 412 miles per hour and the speed of the wind is 18 miles per hour.
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