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)

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**