Together, they can do 1 ship in 4 hours: 1/4Slow Crane can do 1 ship in x hours: 1/xFast Crane can do 1 ship in (x - 6) hours: 1/(x - 6)For our equation we have their separate rates adding together to equal their Together rate:1/x + 1/(x - 6) = 1/4Multiply both sides by the LCD of these fractions, which is 4x(x - 6). Then we have:4(x - 6) + 4x = x(x - 6)Distribute.4x - 24 + 4x = x^2 - 6xCombine like terms.8x - 24 = x^2 - 6xGet all terms to one side and 0 on the other.0 = x^2 - 14x + 24Factor the right side.0 = (x - 12)(x - 2)Set both of these factors equal to 0 and solve for the two x values and you get 12 and 2. We know that the slow one can't possibly load a ship in two hours because that would be less time than they can do it together. So, the slow one takes 12 hours and the fast one takes: x - 6 = 12 - 6 = 6 hours. Let's check these solutions by plugging them into the original equation:1/12 + 1/6 = 1/41/12 + 2/12 = 1/43/12 = 1/41/4 = 1/4Checks out.