1) 25 The ship is moving 20 mph west and 25-10 = 15 mph south. The Pythagorean theorem is then used to find the ship’s speed. The square root of (20 x 20) + (15 x 15) = 25. Therefore the ship is moving at 25 mph. 2) Southwest When you cancel out the forces pushing it North and South, the ship is moving South. It is also moving West, meaning it is moving in the Southwest direction. 3) 1300 5000 2500 The distance from all of these locations is equal to the hypotenuses of a right triangle with the side lengths being equal to the vertical and horizontal distances. Therefore the Pythagorean theorem is used. Tokyo: square root of 1200x1200 + 500x500 = 1300. This is also a multiple of the Pythagorean triple 5, 12, 13. Sydney: square root of 4000x4000 + 3000x3000 = 5000. This is also a multiple of the Pythagorean triple 3, 4, 5. Honolulu: square root of 2000x2000 + 1500x1500 = 2500. This is also a multiple of the Pythagorean triple 3, 4, 5 although this is less obvious. 4) Sydney They are all right triangles so they all have similar shapes. Therefore the only thing that matters in determining which city is the ratio between the two legs of the triangle. For the ship this is 20/15 = 4/3. The city that forms a similar triangle should also have 4/3 when the western part is divided by the southern part. The only city that satisfies this is Sydney, as 4000/3000 = 4/3. The ratio can also be found by dividing the vertical leg by the horizontal leg. In the case of the ship this would be 15/20 = 3/4. Again, the only city with this ratio is Sydney, as 3000/4000 = 3/4. 5) 27 First calculate how far have the robbers gone in 15 hours. Then calculate how much farther they must go to get to Sydney. Then calculate how long that will take. Then answer, how fast does the Besla ship have to go to get there in x hours? The robbers have gone 25x15 = 375 miles. That means they have 5000-375 = 4625 miles left. By rearranging the given equation, Distance/Speed = Time. This can be used to find that the robbers will arrive in Sydney in 4625/25 = 185 hours. The ship needs to travel the full 5000 miles. We again rearrange the equation to get Distance/Time = Speed. This is used to calculate a speed of 5000/185 = 27.03 mph