An airline has 20 airplanes in los angeles, 24 airplanes in st. louis, and 16 airplanes in dallas. during an eight-hour period, 20% of the planes in los angeles fly to st. louis and 10% fly to dallas. of the planes in st. louis, 25% fly to los angeles and 50% fly to dallas. of the planes in dallas, 12.5% fly to los angeles and 50% fly to st. louis. how many planes are in each city after 8 hours?

After 8 hours, there are:

22 planes in Los Angeles

18 planes in St. Louis

20 planes in Dallas

Step-by-step explanation:

Initially, we have

-20 planes in Los Angeles

-24 planes in St. Louis

-16 planes in Dallas

What happens during this period:

20% of the planes in Los Angeles fly to St. Louis:

.

4 planes from Los Angeles fly to St. Louis

and 10% fly to Dallas:

.

2 planes fly from Los Angeles to Dallas.

6 planes leave Los Angeles.

Of the planes in St. Louis, 25% fly to Los Angeles:

.

6 planes fly from St. Louis to Los Angeles.

and 50% fly to Dallas:

.

12 planes fly from St. Louis to Dallas

18 planes leave St. Louis

Of the planes in Dallas, 12.5% fly to Los Angeles:

2 planes fly from Dallas to Los Angeles

and 50% fly to St. Louis:

8 planes fly from Dallas to St. Louis

10 planes leave Dallas.

How many planes arrive at each place?

Los Angeles: 8 planes arrive in Los Angeles, 6 from St. Louis and 2 from Dallas

St. Louis: 12 planes arrive in St. Louis, 4 from Los Angeles and 8 from Dallas.

Dallas: 14 planes arrive in Dallas, 12 from St. Louis and 2 from Los Angeles.

Final result:

Los Angeles:

Initially has 20 airplanes. 6 planes leave and 8 arrive. So

After 8 hours, there are 22 planes in Los Angeles.

St Louis:

Initially has 24 planes. 18 of them leave and 12 arrive. So

After 8 hours, there are 18 planes in St. Louis

Dallas:

Initially has 16 planes. 10 of them leave, and 14 arrive. So:

After 8 hours, there are 20 planes in Dallas.