Question

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?

Answer 1

After 8 hours, there are:

22 planes in Los Angeles

18 planes in St. Louis

20 planes in Dallas

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:

`0.20*20 = 4`.

4 planes from Los Angeles fly to St. Louis

and 10% fly to Dallas:

`0.10*20 = 2`.

2 planes fly from Los Angeles to Dallas.

6 planes leave Los Angeles.

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

`0.25*24 = 6`.

6 planes fly from St. Louis to Los Angeles.

and 50% fly to Dallas:

`0.50*24 = 12`.

12 planes fly from St. Louis to Dallas

18 planes leave St. Louis

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

`0.125*16 = 2`

2 planes fly from Dallas to Los Angeles

and 50% fly to St. Louis:

`0.5*16 = 8`

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

`20 - 6 + 8 = 22`

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

St Louis:

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

`24 - 18 + 12 = 18`

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

Dallas:

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

`16 - 10 + 14 = 20`

After 8 hours, there are 20 planes in Dallas.