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Sagot :
Given:
When flying against a headwind:
Distance = 450 miles
Speed = v - 35 mph
When flying tailwind:
Distance = 702 miles
Speed = v + 35 mph
Let's find the speed of the helicopter.
Apply the formula:
[tex]v=\frac{d}{t}[/tex]Where:
v is the speed
d is the distance
t is the time
Rewrite the equation for time (t):
[tex]t=\frac{d}{v}[/tex]Thus, we have the equations:
Time when flying against headwind:
[tex]t=\frac{450}{v-35}[/tex]Time when flying tailwind:
[tex]t=\frac{702}{v+35}[/tex]Eliminate the equal sides of the equations and combine.
We have:
[tex]\frac{450}{v-35}=\frac{702}{v+35}[/tex]Let's solve for the speed, v.
Cross multiply:
[tex]450(v+35)=702(v-35)[/tex]Apply distributive property:
[tex]\begin{gathered} 450(v)+450(35)=702(v)+702(-35) \\ \\ 450v+15750=702v-24570 \end{gathered}[/tex]subtract 15750 from both sides:
[tex]\begin{gathered} 450v+15750-15750=702v-24570-15750 \\ \\ 450v=702v-40320 \end{gathered}[/tex]Subtract 702v from both sides:
[tex]\begin{gathered} 450v-702v=702v-702v-40320 \\ \\ -252v=-40320 \end{gathered}[/tex]Divide both sides by -252:
[tex]\begin{gathered} \frac{-252v}{-252}=\frac{-40320}{-252} \\ \\ v=160 \end{gathered}[/tex]Therefore, the speed of the helicopter is 160 mph
ANSWER:
s = 160 mph
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