Two ships depart from a port at the same time, one heading south and the other east. Seven hours later, they are separated by a distance of 170 miles. If the ship going south travels 70 miles more than the other, how many miles does each vessel travel?

Answer: 80 miles for the first ship, and 150 miles for the other. Explanation:First thing we should do is correspond each number with a letter:Let x be the distance travel by ship heading eastLet y be the distance travel by ship heading south y = x + 70 -- (1) sqrt(x^2 + y^2) = 170 -- (2)Subtract (1) into (2): sqrt(x^2 + (x + 70)^2) = 170 x^2 + x^2 + 140x + 4900 = 28900 2x^2 + 140x - 24000 = 0 x ^2 + 70x - 12000 = 0 (x - 80)(x + 150) = 0 x = 80 or -150Since the distance for the first ship can’t be negative, therefore, x = 80 -- (3)Subtract (3) into (1), therefore, y = 150Hope this helps! :)