2 trains leave the same train station at the same time, one train travels northeast at 50 mph, the other train travels due west at 40 mph, how far apart are the trains after two hours

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360 miles per hour

180 To find the distance between the two trains after two hours, we need to calculate the distance traveled by each train during that time.

The first train is traveling northeast at 50 mph. "Northeast" means it is moving in the direction halfway between north and east. Since both north and east are at right angles to each other, we can say that the train is moving at a 45-degree angle to the north or east direction.

To find the distance traveled by the first train after two hours, we need to determine the component of its velocity in the north and east directions. Since it is moving at a 45-degree angle, we know that the northward component and eastward component are the same.

Using trigonometry, we can calculate the northward and eastward components:

northward component = velocity * cos(45 degrees) = 50 mph * cos(45 degrees)
eastward component = velocity * sin(45 degrees) = 50 mph * sin(45 degrees)

Now, the train has been traveling for 2 hours, so the distance traveled in each direction is:

northward distance = northward component * time = northward component * 2 hours
eastward distance = eastward component * time = eastward component * 2 hours

Similarly, for the second train, which is traveling due west at 40 mph, we can find the distance traveled after 2 hours:

westward distance = velocity * time = 40 mph * 2 hours

To find the total distance between the trains, we can use the Pythagorean theorem. The distance between the two trains is the hypotenuse of a right triangle, with the northward distance as one side, the eastward distance as the other side, and the westward distance as the base:

total distance = square root of ((northward distance)^2 + (eastward distance)^2 + (westward distance)^2)

Now we can substitute the calculated values and solve for the total distance between the two trains.