Respuesta :
The Solution:
Let the speed without the tailwind (wind) be represented with x.
And let the speed of the wind be represented with y.
The Speed without wind:
Given that a jet can only fly 2408 miles in 4 hours.
By formula,
[tex]S=\frac{D}{T}[/tex]Where,
D = distance = 2408 miles
T = time = 4 hours
S = (x - y) miles/hour
Substituting these values in the formula, we get
[tex]\begin{gathered} x-y=\frac{2408}{4} \\ \text{ Cross multiplying, we get} \\ 4(x-y)=2408 \end{gathered}[/tex]Dividing both sides by 4, we get
[tex]x-y=602\ldots\text{eqn}(1)[/tex]Similarly,
The Speed with the wind:
Given that the jet fly 2704 miles in 4 hours with a tailwind.
Again, the formula:
[tex]S=\frac{D}{T}[/tex]Where,
D = distance = 2704 miles
T = time = 4 hours
S = (x + y) miles/hour
Substituting these values in the formula, we get
[tex]\begin{gathered} x+y=\frac{2704}{4} \\ \\ x+y=676\ldots\text{eqn}(4) \end{gathered}[/tex]Solving both equations as simultaneous equations.
[tex]\begin{gathered} x-y=602\ldots\text{eqn}(1) \\ x+y=676\ldots\text{eqn}(2) \end{gathered}[/tex]By the elimination method, we shall add their corresponding terms together in order to eliminate y.
[tex]\begin{gathered} x-y=602 \\ x+y=676 \\ -------- \\ 2x=1278 \end{gathered}[/tex]Dividing both sides by 2, we get
[tex]x=\frac{1278}{2}=639\text{ m/h}[/tex]Thus, the speed of the jet in still air (without wind) is 639 miles/hour.
To solve for y:
We shall substitute 639 for x in eqn(2)
[tex]\begin{gathered} x+y=676 \\ 639+y=676 \end{gathered}[/tex]Collecting the like terms, we get
[tex]y=676-639=37\text{ m/h}[/tex]Therefore, the speed of the wind is 37 miles/hour.
