Polynomial, Rational & Absolute Value Equations

Question

A plane travels 700mi from Los Angeles, California, to Santa Fe, New Mexico, with a prevailing wind of 32 mph. The return trip against the wind takes 13 hr longer. Find the average speed of the plane in still air.

Answer 1

700 = (r+32)*(t) <--- with the wind

700 = (r-32)*(t+13) <-- against the wind

first equation says:

t = 700/(r+32)

plugs into second equation:

700 = (r-32) [700/(r+32) + 13]

= (r-32) [700 + 13(r+32)]/(r+32)

= (r-32)[ 700 + 13r + 416]/(r+32)

700(r+32) = (r-32)(13r + 1116)

700r + 22400 = 13r^2 + 1116r - 416r - 35712

0 = 13r^2 - 58112

r=66.8592