Pretty much any airplane can easily fly in 25 mph winds. If that is a direct crosswind that might make landing smaller aircraft more challenging, but airliners, no problems.
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There is no single maximum wind limit as it depends on the direction of wind and phase of flight. A crosswind above about 40mph and tailwind above 10mph can start to cause problems and stop commercial jets taking off and landing.
If the airline cancels your flight or it's significantly delayed (a term currently defined on a case-by-case basis) and you're forced to change your travel plans, the Department of Transportation requires airlines to provide a full refund. Unfortunately, getting a refund is often a lengthy and frustrating process.
If there is a tail wind of 10mph from behind, then the aircraft needs to be going 80mph (ie 70mph relative speed for those conditions) to get airborne. Similarly, if you are taking off into a 10mph headwind, then you only need to be going 60mph to fly.
The 737 has been designed to withstand landings at 600fpm, reducing to 360fpm at MLW before a hard landing inspection is required. Most pilots report a hard landing when the sink rate exceeds approximately 240fpm.