Question

A plane travels at a speed of 205mph in still air. Flying with a tailwind, the plane is clocked over a distance of 975 miles. Flying against a headwind, it takes 2 hours longer to complete the return trip. What was the wind velocity?

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Answer 1

T1 = 975 / (205 + V) flying with wind

T2 = 975 / (205 - V) flying against wind

T2 = T1 + 2

975 * {1 / (205 - V) - 1 / (205 + V)] = 2

(205 + V + V -205) / (205^2 - V^2) = 2 / 975

V^2 + 975 V - 42025 = 0 rearranging

V = 41.3

Values of flying are 246.3 and 163.7

Check:

T1 = 975 / 246.3 = 3.96 hrs

T2 = 975 / 163.7 = 5.96 hrs