13. If two planes leave the same airport at 1:00 PM, how many miles apart will they be at 3:00 PM if one travels directly north at 150 mph and the other travels directly west at 200 mph?
A. 50 miles
B. 100 miles
C. 500 miles
D. 700 miles
E. 1,000 miles
One will travel 300 miles and other 400 miles.
Imagine these are two sides of a right angle triangle. Then use the Pythagorean theorem to find their distance apart. We'll be glad to check your answer.
To find the solution to this problem, we can use the concept of vector addition. We know that one plane is traveling directly north at 150 mph, and the other plane is traveling directly west at 200 mph.
First, let's calculate how far each plane will travel in 2 hours (from 1:00 PM to 3:00 PM). Since one plane is traveling north at 150 mph, it will cover a distance of 150 * 2 = 300 miles in those 2 hours. Similarly, the other plane traveling west at 200 mph will cover a distance of 200 * 2 = 400 miles.
Now, we can use the Pythagorean theorem to find the distance between the two planes. The distance between them will be the hypotenuse of a right-angled triangle formed by the northward and westward distances traveled by each plane.
The distance between them can be calculated as follows:
Distance^2 = (300 miles)^2 + (400 miles)^2
Distance^2 = 90000 miles^2 + 160000 miles^2
Distance^2 = 250000 miles^2
Distance ≈ 500 miles
Therefore, the planes will be approximately 500 miles apart at 3:00 PM. Hence, the correct answer is option C.