Let us assume the speed of the Jet = x mph.
Step 1: Given the speed of the Jet = 35mph.
Total speed of the jet with tailwind = (x+35)mph
Total speed of the jet with headwind = (x-35)mph
Step 2: To calculate using distance-time relationship
[tex]\text{time = }\frac{distance}{speed}[/tex][tex]\begin{gathered} \text{Time taken against the headwind = }\frac{1120}{(x-35)} \\ \text{Time taken against the headwind = }\frac{1568}{(x+35)} \end{gathered}[/tex]Step 3: Equate both since the two times taken for the journey are the same,
Hence
[tex]\begin{gathered} \frac{1120}{x-35}=\frac{1568}{x+35} \\ \text{cross multiply} \\ 1120(x+35)\text{ = 1568(x-35)} \\ 1120x+39200\text{ = 1568x - 54880} \\ \text{collect like terms} \\ 39200+54880\text{ = 1568x-1120x} \\ 94080\text{ = 448x} \\ dividebothside\text{ } \\ x\text{ = }\frac{94080}{448} \\ x\text{ =210} \end{gathered}[/tex]Therefore the speed of the jet = 210mph
