Set up appropriate systems of two linear equations in two unknowns and then solve the systems by determinants. All numbers are accurate to at least two significant digits.

The velocity of sound in steel is 15,900ft/s faster than the velocity of sound in air. One end of a long steel bar is struck, and an instrument at the other end measures the time it takes for the sound to reach it. The sound in the bar takes 0.0120s, and the sound in the air takes 0.180s. What are the velocities of sound in air and in steel?