Wind blows with a velocity `x` in the direction shown in (Fig. 5.137). Two aeropalnes starts out from point `A` and fly with a constant speed `y`. The first flies from `A to B` and the other `A to C`. Both of them return back to `A`. If `AB = AC`, then which plane will return to point `A` first, and what be the ratio of the times of flight of the two planes ?
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Explanation

Time taken from `A` to `B` than `B` to `A`,
`t_((AB//BA)) = (AB)/(y - x) + (A B)/(y + x) = (2 y(A B))/(y^2 - x^2)`
Time taken from `A` to `C` than `C` to `A`,
`t_((AC//CA)) = (2 A C)/(sqrt(y^2 - x^2))R`
Ratio of times `= (y)/(sqrt(y^2 - x^2)) = (1)/(sqrt(1 - x^2//y^2)) gt 1`
Hence, the first plane takes more time.
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