Question

Two ships leave port at the same time. One heads due north and the other heads due east. Later, the two boats are exactly 100 km apart. The ship headed north has traveled 20 km farther than the ship going east. How far has the ship going east traveled?

Answer 1

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Explanation:

Answer 2

N

A (North)
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O-----------------B (East)

OAB is a right triangle with the hypotenuse AB = 100 km
Le x be OB, the distance travelled East, the distance OA travelled North
is x+20 (given)
Now apply Pythagoras:

AB² = OA² + OB² ↔ 100² = (x+20)² + x²
After expanding you'll find:
2x²+40x-9600 = 0. Solve this quadratic equation and you will find :

x' = 60 and x" = -80 (extraneous). Hence OB = x = 60 km