Final answer:
The speed of the southbound plane is 142.4 mph, and the speed of the northbound plane, which is faster by 30 mph, is 172.4 mph. This is calculated by using the distance equals speed multiplied by time formula with the given total distance and time.
Step-by-step explanation:
To find the speed of each plane, we need to set up an equation based on the information provided. Let's denote the speed of the southbound plane as s and the speed of the northbound plane as s + 30 mph since it's traveling 30 mph faster. As they are going in opposite directions, their relative speed when moving away from each other is sum of their speeds.
We know that distance (d) equals speed (v) multiplied by time (t), so we have:
- d = (s + (s + 30)) × t
- d = (2s + 30) × 2.5 hours
- 1855 miles = (2s + 30) × 2.5 hours
Now we solve for s:
- 1855 miles = (5s + 75) hours
- 1855 miles - 75 = 5s × 2.5 hours
- 1780 = 12.5s
- s = 142.4 mph
Therefore, the southbound plane's speed is 142.4 mph, and the northbound plane's speed is 142.4 mph + 30 mph, which equals 172.4 mph.