Cycling a mile with and against the wind

A cyclist covers one mile in $3$ minutes with a tailwind and in $4$ minutes into a headwind of the same strength. Assuming the wind simply adds to or subtracts from his speed, how long would the mile take in still air?

$\tfrac{24}{7}$ minutes (about 3.43). His speeds are $\tfrac13$ and $\tfrac14$ miles per minute, and the still-air speed is their average, $\tfrac{7}{24}$ miles per minute. So the mile takes $\tfrac{24}{7}$ minutes, not the naive $3.5$.