2 ships sail from the same por, one sails dew east at 15 mph and the second sailed dew south at 20 mph, how far apart are the ships after 3 hours? could you show the how you set this problem up?
They sail in perpendicular directions. The line connecting their locations is always the hypotenuse of a right triangle with perpendicular legs. After 3 hours, the legs of the triangle are 45 and 60 miles.
The hypotenuse (distance between them) is 75 miles at that time, according to the Pythagorean theorem.
To determine how far apart the ships are after 3 hours, we need to find the distance traveled by each ship in the respective directions.
The first ship sails due east at a speed of 15 mph. Since it sails for 3 hours, the distance it covers can be calculated by multiplying its speed (15 mph) by the time (3 hours), giving us: 15 mph * 3 hours = 45 miles.
The second ship sails due south at a speed of 20 mph. Similar to the first ship, the distance it covers is obtained by multiplying its speed (20 mph) by the time (3 hours), resulting in: 20 mph * 3 hours = 60 miles.
Now we have a right-angled triangle, with the distances traveled by the two ships as its sides. Using the Pythagorean theorem, we can calculate the distance between the two ships. The theorem states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the distance between the ships represents the hypotenuse, while the distances traveled by each ship form the other two sides of the triangle.
Therefore, the distance between the ships is given by: √(45^2 + 60^2) = √(2025 + 3600) = √5625 = 75 miles.
Therefore, the ships are 75 miles apart after 3 hours.