A plane leaves Chicago headed for Los Angeles at 520 mph. One hour later, a second plane leaves Los Angeles headed for Chicago at 620 mph. If the air route from Chicago to Los Angeles is 1800 miles, how long will it take (after the first plane takes off) for the first plane to pass the second plane? (Round your answer to two decimal places.)

Question

A plane leaves Chicago headed for Los Angeles at 520 mph. One hour later, a second plane leaves Los Angeles headed for Chicago at 620 mph. If the air route from Chicago to Los Angeles is 1800 miles, how long will it take (after the first plane takes off) for the first plane to pass the second plane? (Round your answer to two decimal places.)

Answer 1

520 t + 620 (t-1) = 1800

Answer 2

To solve this problem, we need to figure out how long it will take for the two planes to meet.

Let's start by finding out how long it will take for the first plane to travel from Chicago to the meeting point. Since the first plane has a speed of 520 mph and the distance from Chicago to the meeting point is 1800 miles, we can use the formula:

time = distance / speed

time = 1800 miles / 520 mph

Let's calculate that:

1800 miles / 520 mph = 3.46 hours

So, it will take the first plane 3.46 hours to travel from Chicago to the meeting point.

Now, let's find out how long it will take for the second plane to travel from Los Angeles to the meeting point. Since the second plane has a speed of 620 mph and has a one-hour head start, the distance it needs to travel is the same as the distance between Chicago and the meeting point. So we can use the same formula to find the time it takes for the second plane to reach the meeting point:

time = distance / speed

time = 1800 miles / 620 mph

Let's calculate that:

1800 miles / 620 mph = 2.9 hours

So, it will take the second plane 2.9 hours to travel from Los Angeles to the meeting point.

Now, to find out how long it will take for the first plane to pass the second plane, we need to subtract the time it took for the second plane to reach the meeting point from the time it took for the first plane to reach the meeting point:

time = time taken by the first plane - time taken by the second plane

time = 3.46 hours - 2.9 hours

Let's calculate that:

3.46 hours - 2.9 hours = 0.56 hours

So, it will take the first plane 0.56 hours (or 0.56 * 60 minutes = 33.6 minutes) to pass the second plane after the first plane takes off from Chicago.