Respuesta :
Let speed of plane be "x" and speed of wind be "w".
• With the wind, the speed of plane becomes:
x + w
• Against the wind, the speed of plane becomes:
x - w
We know D = RT, where
D is distance
R is rate
T is time
Going against the wind, it takes 7 hours, so we can write:
[tex]\begin{gathered} 6300=(x-w)7 \\ 7x-7w=6300 \end{gathered}[/tex]Going with the wind, it takes 6 hours, thus:
[tex]\begin{gathered} 6300=(x+w)6 \\ 6x+6w=6300 \end{gathered}[/tex]Let's multiply the first equation by 6 and the second equation by 7:
[tex]\begin{gathered} 6\times(7x-7w=6300) \\ 42x-42w=37800 \\ \text{and} \\ 7\times(6x+6w=6300) \\ 42x+42w=44100 \end{gathered}[/tex]Adding the two new equations, we can eliminate w and solve for x:
[tex]\begin{gathered} 42x-42w=37,800 \\ 42x+42w=44,100 \\ ---------------- \\ 84x=81900 \\ x=975 \end{gathered}[/tex]We can use this value of x and put it into the first equation and solve for w:
[tex]\begin{gathered} 7x-7w=6300 \\ 7(975)-7w=6300 \\ 6825-7w=6300 \\ 7w=525 \\ w=75 \end{gathered}[/tex]Thus,
AnswerSpeed of Plane = 975 km/hr
Speed of Wind = 75 km/hr
