A plane leaves Chicago headed for LA at 540 mph. One hour later, a second plane leaves LA headed for Chicago at 660 mph. If the air route from Chicago to LA is 1800 miles, how long will it take for the first plane to pass the second plane? How far from Chicago will they be at that time?

if we call x the flying time for the 2nd plane, then since distance = speed * time,

660x + 540(x+1) = 1800
x = 1.05 hours

So, how far did the first plane travel in 2.05 hours?

To find out when the two planes will pass each other and how far from Chicago they will be at that time, we can set up an equation based on their speeds and the given distance.

Let's assume that it takes the first plane (Plane A) and the second plane (Plane B) t hours to meet after Plane A leaves Chicago. Since Plane A leaves one hour earlier, Plane B has been flying for t - 1 hours.

First, we need to find out how far each plane has traveled when they meet.

The distance traveled by Plane A can be calculated as follows:
Distance_A = Speed_A * Time_A
Distance_A = 540 * t

The distance traveled by Plane B can be calculated as follows:
Distance_B = Speed_B * Time_B
Distance_B = 660 * (t - 1)

Both planes will meet when their distances add up to the entire distance between Chicago and LA, which is 1800 miles:
Distance_A + Distance_B = 1800
540t + 660(t - 1) = 1800

Simplifying the equation:
540t + 660t - 660 = 1800
1200t = 2460
t = 2460 / 1200
t ≈ 2.05 hours

Since we can't have 0.05 of an hour, let's convert it to minutes:
0.05 hours * 60 minutes/hour = 3 minutes

Therefore, it will take approximately 2 hours and 3 minutes for the first plane to pass the second plane.

To find out how far from Chicago they will be at that time, we can substitute the value of t into either of the distance formulas.

Using the formula for Plane A:
Distance_A = 540 * t
Distance_A = 540 * 2.05 ≈ 1107 miles

Therefore, when the planes pass each other, they will be approximately 1107 miles from Chicago.