Final answer:
The two planes will be 125 miles apart 1 hour after noon. We get this by adding their speeds and dividing the distance they must cover prior to being 125 miles apart by the combined speed.
Step-by-step explanation:
The question involves determining the time two planes will be 125 miles apart when one leaves New York for Orlando and one leaves Orlando for New York. The distance from New York to Orlando is 1300 miles. The New York plane's speed is 450 mph, and the Orlando plane flies at 490 mph. To solve the problem, we add the speeds of the planes because they are moving towards each other, resulting in a combined speed of 940 mph.
We then divide the distance they must cover before they are 125 miles apart, which is 1300 - 125 = 1175 miles, by the combined speed to find the time it will take for them to be this distance apart. Therefore, we calculate 1175 miles / 940 mph = 1.25 hours. Since the planes left precisely at noon, adding 1.25 hours to this we get 1:15 PM, which can be rounded to 1 hour after noon.