Answer:
The speed of the jet is 175 mph
Step-by-step explanation:
Let x be the speed of the jet.
The speed of the wind is 18 mph.
If the jet can fly 942 miles against the headwind:
[tex]x=\frac{942}{t}+18\text{ \lparen1\rparen}[/tex]If it can fly 1158 nukes with an 18 mph tailwind, therefore:
[tex]x=\frac{1158}{t}-18\text{ \lparen2\rparen}[/tex]Equalize, and solve for t using equations (1) and (2).
[tex]\begin{gathered} \frac{942}{t}+18=\frac{1158}{t}-18 \\ \frac{942}{t}-\frac{1158}{t}=-18-18 \\ -\frac{216}{t}=-36 \\ t=\frac{-216}{-36} \\ t=6\text{ hours} \end{gathered}[/tex]Now, knowing the time substitute it into the equation and solve for the speed of the jet.
[tex]\begin{gathered} x=\frac{1158}{t}-18 \\ x=175\text{ mph} \end{gathered}[/tex]The speed of the jet is 175 mph.
