there are two planes. they both leave the airport at 1pm. one plane travels north at 150mph and the other plane travels west at 200mph. how many miles will they be apart at 3pm?

One plane will be 300 miles away; the other will be 400 miles away.

Consider this a right triangle and use the Pythagorean theorem to find the hypotenuse.

To find out how many miles the two planes will be apart at 3pm, we can use basic trigonometry and the concept of relative velocity.

Step 1: Determine the time difference
Both planes leave the airport at 1pm, so the time difference between their departure and 3pm is 2 hours.

Step 2: Calculate the distance each plane has traveled
Plane 1 (traveling north):
Since Plane 1 travels at a constant speed of 150 mph for 2 hours, the distance it covers is:
Distance = Speed × Time = 150 mph × 2 hours = 300 miles

Plane 2 (traveling west):
Similarly, Plane 2 travels at a constant speed of 200 mph for 2 hours, so its distance covered is:
Distance = Speed × Time = 200 mph × 2 hours = 400 miles

Step 3: Apply Pythagoras' theorem
To find the distance between the two planes, we can draw a right-angled triangle with the two distances as its sides. The third side of this triangle represents the distance between the planes.

Using Pythagoras' theorem (a^2 + b^2 = c^2), where a and b are the distances covered by each plane, and c is the distance between them, we can find c.

Distance^2 = 300^2 + 400^2 = 90,000 + 160,000 = 250,000

Taking the square root of both sides, we find:
Distance = √250,000

Hence, the two planes will be approximately 500 miles apart at 3pm.