Final answer:
The two airplanes meet approximately 325.2 miles away from Denver. This is calculated by considering their combined speed and the distance each would cover before meeting.
Step-by-step explanation:
To determine how far they are from Denver when they meet, we need to consider the combined rate at which the two planes are approaching each other and the time difference between their departures.
The first plane leaves Los Angeles for Denver at a speed of 440 mph, and half an hour later, the second plane leaves Denver for Los Angeles at a speed of 470 mph. The combined speed of the two planes is 440 mph + 470 mph = 910 mph. The second plane departs 0.5 hours after the first, so in that time, the first plane will travel 440 mph × 0.5 hours = 220 miles towards Denver.
At the time the second plane starts, there is a distance of 850 miles - 220 miles = 630 miles between them. We need to find out how long it will take for the two planes to cover this distance at the combined speed of 910 mph. The time taken will be 630 miles ÷ 910 mph = 0.6923 hours (approximately).
The distance the second plane travels in this time is 470 mph × 0.6923 hours = 325.2 miles (approximately). Therefore, the point where they meet is 850 miles - 325.2 miles = 524.8 miles from Los Angeles. Consequently, since the distance between Los Angeles and Denver is 850 miles, the distance from Denver when they meet is 850 miles - 524.8 miles = 325.2 miles (approximately).