An airplane leaves Atlanta at 2 PM and flies north at 250 miles per hour. A second airplane leaves Atlanta 30 minutes later and flies north at 280 miles per hour. At what time will the second airplane overtake the first?

Answer Choices
6:20 PM
6:00 PM
6:40 PM
6:50 PM
7:10 PM

250mi/h * 0.5h = 125 mile head start.

280T = 125 + 250T.
30T = 125, T = 4.17 Hours. = 4h and 10 Min. to catchup.

2:30 + 4:10 = 6:40 PM.

Well, this sounds like a classic case of planes playing catch-up! Let's do some math, but I'll sprinkle in a little humor to keep things entertaining.

The first airplane flies for a whole 30 minutes before the second one even takes off. That's like giving the first plane a head st-ART! *Giggles*

Now, we know that the first plane is flying at 250 mph, and the second is zipping at 280 mph. So, every hour that goes by, the second plane gains a 30-mile advantage on the first one. That's like a little sibling trying to overtake the older sibling in a race! So determined!

To figure out when they'll meet up, we need to figure out how long it takes the second plane to close that 30-mile gap. If we divide the 30-mile advantage by the speed difference between the two planes (280 - 250 = 30), we get 1 hour. So, the second plane will catch up to the first in just 1 hour!

Considering the second plane departs 30 minutes after 2 PM, it will overtake the first plane at 3:30 PM. But wait, we need to convert that back to boring old numbers, right? So, our answer is 3:30 PM.

Oops, hold on a sec! We need to add that 30 minutes the second plane was behind the first one. So, when we add 30 minutes to 3:30 PM, we get... *drum roll, please*... 4:00 PM as the time when the second plane overtakes the first one!

Therefore, the correct answer is none of the above. I guess the joke's on the answer choices this time! *Chuckles*

To find the time when the second airplane overtakes the first, we need to determine the distance the first airplane has traveled in that time period.

The first airplane flies at a speed of 250 miles per hour for 30 minutes longer than the second airplane, which means it has a head start.

Let's calculate the distance traveled by the first airplane in those 30 minutes:
Distance = Speed × Time
Distance = 250 miles/hour × (30 minutes / 60 minutes)
Distance = 250 miles/hour × 0.5 hour
Distance = 125 miles

Now, we need to find the time it takes for the second airplane to cover this distance and overtake the first airplane.

The relative speed between the two airplanes is the difference in their speeds:
Relative Speed = Speed of second airplane - Speed of first airplane
Relative Speed = 280 miles/hour - 250 miles/hour
Relative Speed = 30 miles/hour

To find the time it takes for the second airplane to cover the 125-mile distance:
Time = Distance / Relative Speed
Time = 125 miles / 30 miles/hour
Time = 4.17 hours

Now, we add this time to the initial departure time of the second airplane to find the overall time when the second airplane overtakes the first.

2 PM + 4.17 hours = 6:10 PM (approximately)

Therefore, the second airplane will overtake the first airplane at approximately 6:10 PM.

Since none of the answer choices provided matches exactly, we can conclude that the closest option is 6:10 PM, but it is not listed.

the answer is obviously 6:40 henry goes in to detail onto why that is.

6:20