In order to fully understand the problem, it is best to sketch it. Sketching the system, we will see that the system forms a triangle where the angle of elevation is 36 degrees. We are asked to find the hypotenuse. We can use a trigonometric function. It should be noted that one of the sides should also be given in order to calculate the hypotenuse. Trigonometric functions that can be used are:

sin(theta) = opposite / hypotenuse
cos(theta) = adjacent / hypotenuse

7 0

3 years ago

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a plane flying with the wind travels 630 mi in 1.5hrs. Flying against the wind , the plane travels 1120 mi in 4hrs. Find the rat

Flauer [41]

$\bf \begin{cases}
r=\textit{rate of the plane}\\
w=\textit{rate of the wind}\\
\end{cases}
\\\\

\begin{array}{ccccllll}
&distance&rate&time(hrs)\\
&\textendash\textendash\textendash\textendash\textendash\textendash&\textendash\textendash\textendash\textendash\textendash\textendash&\textendash\textendash\textendash\textendash\textendash\textendash\textendash\textendash\textendash\\
\textit{with wind}&630&r+w&1\frac{1}{2}\\
\textit{against wind}&1120&r-w&4
\end{array}
$

$\bf thus \begin{cases}
630=(r+w)1\frac{1}{2}\to 630=(r+w)\frac{3}{2}
\\\\
1120=(r-w)4\\
--------------\\
630=(r+w)\frac{3}{2}\implies 630\cdot \frac{2}{3}=r+w\\
420=r+w\implies \boxed{420-w}=r\\
--------------\\
thus\\
--------------\\
1120=(r-w)4\implies 1120=4r-4w
\\\\
1120=4(\boxed{420-w})-4w
\end{cases}
$

solve for "w", to find the wind's speed rate,

so hmmm what's the plane's rate? well 420 - w = r :)

5 0

2 years ago