Two boats leave a dock at the same time, one traveling due south and the other due west. Later, the boats are 75 miles apart. If The boat traveling due south travelled 30 miles farther than the other boat, how many miles did each boat travel??

Question

mww · Answer

try to draw the situation. You should end up with a right angled triangle and the hypotenuse being the final distance between the boats.
Let x be the distance travelled west. Then distance travelled south is 30 more than this so must be x+30.

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Then put these into Pythagoras' theorem.

$$DW^2 + SW^2 = 75^2 = x^2 + (x+30)^2$$

Expand and solve for x (may use Quadratic formula)