Step 1
Write a system of equations from the question.
Let x = speed of the plane in still air
y = speed of jetstream
[tex]\begin{gathered} \text{Speed with jet}stream=x+y \\ \text{Speed }against\text{ jetstream=x-y} \end{gathered}[/tex]
[tex]\begin{gathered} \text{Distance}=rate(\text{time)} \\ \text{Time therefore=}\frac{\text{Distance}}{\text{rate}} \end{gathered}[/tex]
For the first instance with the jetstream;
[tex]\begin{gathered} \frac{6296}{x+y}=8 \\ 6296=8(x+y)---(1) \end{gathered}[/tex]
For the second instance against the jetstream;
[tex]\begin{gathered} \frac{5416}{x-y}=8 \\ 5416=8(x-y)---(2) \end{gathered}[/tex]
Step 2
Solve for x. Add equation 1 to 2
[tex]\begin{gathered} 6296=8x+8y---(1) \\ 5416=8x-8y---(2) \\ 11712=16x \\ \frac{16x}{16}=\frac{11712}{16} \\ x=732\text{miles per hour} \end{gathered}[/tex]
Step 3
Solve for y
Substitute for x in equation 1
[tex]\begin{gathered} 6296=8(732)+8y \\ 6296=5856+8y \\ 6296-5856=8y \\ 440=8y \\ \frac{8y}{8}=\frac{440}{8} \\ y=55\text{ miles per hour.} \end{gathered}[/tex]
Rate of the jet in still air=732miles per hour
Rate of the jetstream=55 miles per hour
