Two ships leave port at the same time, one heading due south and the other heading due east.

Several hours after departure the two ships described are 195 miles apart. If the ship traveling south traveled 105 miles father than the other, how many miles did they each travel ?

Solution:

                      East ship travelled = x miles

                        South ship travelled = x + 105  miles

                  x^2  + (x+105)^2  = (195)^2

               2x^2 + 210x + 11025 = 38028

               2x^2 + 210x - 27000 = 0

                 x^2 + 105x - 13500 = 0

                  x^2 + 180x - 75x - 13500 = 0

              (x+180)(x-75) = 0

                  x = 75 miles for east

             x + 105 = 180 miles for south