A commuter plane leaves an airport and travels due south at 375 mph. Another plane leaves at the same time and travels due east at 500 mph. Find the distance between the two planes after 2 h.

Question

A commuter plane leaves an airport and travels due south at 375 mph. Another plane leaves at the same time and travels due east at 500 mph. Find the distance between the two planes after 2 h.

Answer 1

since mph means miles per 1 hour and we are looking for the distance between the two planes after 2 hours, our first step is to multiply 375 and 500 by 2 to get 750 miles (375 x 2) for the plane heading due south and 1000 miles (500 x 2) for the plane heading due east.

Since both of these numbers create two sides of a triangle, our next step is to use the Pythagorean Theorem. The Pythagorean Theorem will make it so that we multiply 750 miles by itself to get 562,500 for the side heading due south and multiply 1000 miles by itself to get 1,000,000 for the side heading due east. Now we will add 562,500 and 1,000,000 to get 1,562,500 for the third side, which is the distance between the two planes, or the hypotenuse of the triangle. Finally, we take the square root of 1,562,500 to get 1250 miles between the two planes.

Answer 2

An airplane leaves the origin heading south at 375 mph. Since it travels for two hours, that means it will simply travel 750 miles. Well, the eastbound plane is going 500 mph. So because it traveled for two hours, it traveled only 1000 miles in the distance between those two planes. We just jaggery the hole in, uh, triangle. So in a square of 750 plus 1000 squares, it will be equal to C squared, which is equal to 1562500 squares. If we take the square root of that it will be the distance R C, So the square root of 1562500 will equal 1250 miles. Okay, so the planes fly out 1250 miles after two hours. Many thanks.