The Solution:
Let the speed of the jet without the wind be x and the speed of the wind be y.
By formula,
[tex]\text{ Speed (S) =}\frac{\text{ distance (d) }}{\text{ time (t) }}[/tex]So,
With the Tailwind:
d=distance = 2660 miles
t=time = 4 hours
s = speed = (x+y) m/h
Substituting these values in the formula above, we get
[tex]\begin{gathered} (x+y)=\frac{2660}{4} \\ \\ x+y=665\ldots\text{eqn}(1) \end{gathered}[/tex]Wind the Headwind:
d = 2492 miles
t = 4 hours
speed = (x-y) m/h
Substituting, we get
[tex]\begin{gathered} (x-y)=\frac{2492}{4} \\ \\ x-y=623\ldots\text{eqn}(2) \end{gathered}[/tex]Solving eqn(1) and eqn(2) simultaneously by the Elimination Method.
[tex]\begin{gathered} x+y=665 \\ x-y=623 \\ -------- \\ 2x=1288 \end{gathered}[/tex]Dividing both sides by 2, we get
[tex]x=\frac{1288}{2}=644\text{ miles/hour}[/tex]Thus, the speed of the jet is 644 miles/hour.
The speed of the wind ( the value of y):
We shall substitute 644 for x in eqn(1).
[tex]\begin{gathered} 644+y=665 \\ y=665-644 \\ y=21\text{ miles/hour} \end{gathered}[/tex]Therefore, the speed of the wind is 21 miles/hour.