Aventar (ah-venn-TAR, lit. to throw) is used in three very popular ways. The first is aventarse (lit. to throw oneself). It means to take one's chances and do something adventurous. A person that often exhibits that behavior is referred to as aventado or aventada. The second form is aventón (lit. big push). It means car ride. If one is given an aventón, one is hitching a ride. The proper way to ask for a ride is "¿me das un aventón?" (can you give me a big push?). In Mexico City you must not ask an aventón to people you do not know, not because is inappropriate but because it is dangerous. The third way is al aventón. It means to do something in a rush and, consequently, in a substandard way.
Un estudiante a otro: Ese cuate es bien aventado. ¡Le pidio un aventón a la esposa del maestro!
One student to another: That dude is fearless. He asked the teacher's wife a ride!
Maestro: Esta tarea no corresponde a un estudiante con sus capacidades y su curiosidad intelectual.
Estudiante: Es que la hice al aventón.
Teacher: This homework is not what I expect from someone with your skills and intellectual curiosity.
Student: I really didn't spend much time preparing it.
The young lady in the image below is at Circuito Interior trying to get an aventón to Juchitan. Most likely she is not from D.F.