Question

A private jet can fly 1120 miles against a 35-mph headwind in the same amount of time it can fly 1568 miles with a 35-mph tailwind. Find the speed of the jet.

Answer 1

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

`\text{time = }(distance)/(speed)`
`\begin{gathered} \text{Time taken against the headwind = }(1120)/((x-35)) \\ \text{Time taken against the headwind = }(1568)/((x+35)) \end{gathered}`

Step 3: Equate both since the two times taken for the journey are the same,

Hence

`\begin{gathered} (1120)/(x-35)=(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{ = }(94080)/(448) \\ x\text{ =210} \end{gathered}`

Therefore the speed of the jet = 210mph