Two planes leave the airport at the same time. One plane heads directly south at 550 mph. The other plane heads directly west at 300 mph. Assuming both fly at the same elevation, how quickly is the distance between them increasing 3 hours after takeoff (rounded to the nearest mile per hour)? (1 point) Responses 626 mph 626 mph 1,879 mph 1,879 mph 1,535 mph 1,535 mph 71 mph 71 mph 483 mph
To solve this problem, we can use the Pythagorean theorem.
Let's call the distance between the two planes at any given time "d".
After 3 hours, the southbound plane will have traveled 550 mph * 3 hours = 1650 miles.
After 3 hours, the westbound plane will have traveled 300 mph * 3 hours = 900 miles.
By the Pythagorean theorem, we have:
d^2 = (1650^2) + (900^2)
d^2 = 2722500 + 810000
d^2 = 3532500
d = 1879.5 miles (rounded to the nearest mile).
Therefore, the distance between the two planes is increasing at a rate of approximately 1879 miles per hour.