A coworker at the plasma TV factory drives 15 mph faster than you. In the same time that the coworker travels 12 miles, you travel 7.5 miles to work. How fast is your coworker driving?

If we allow 'x' to represent the co-worker's speed, we can deduce the following:

12/x = 7.5/(x - 15)  (your statement)
12(x - 15) = 7.5x  (cross multiply)
12x - 180 = 7.5x  (eliminate parenthesis by applying the distributive property)
12x - 180 + 180 = 7.5x + 180  (add 180 to both sides)
12x = 7.5x + 180  (collect terms)
12x - 7.5x = 7.5x - 7.5x + 180  (subtract 7.5x from both sides)
4.5x = 180  (collect terms)
4.5x/4.5 = 180/4.5  (isolate the variable by dividing both sides by 4.5)
x = 40 mph