Respuesta :
Answer:
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:
[tex]0.20*20 = 4[/tex].
4 planes from Los Angeles fly to St. Louis
and 10% fly to Dallas:
[tex]0.10*20 = 2[/tex].
2 planes fly from Los Angeles to Dallas.
6 planes leave Los Angeles.
Of the planes in St. Louis, 25% fly to Los Angeles:
[tex]0.25*24 = 6[/tex].
6 planes fly from St. Louis to Los Angeles.
and 50% fly to Dallas:
[tex]0.50*24 = 12[/tex].
12 planes fly from St. Louis to Dallas
18 planes leave St. Louis
Of the planes in Dallas, 12.5% fly to Los Angeles:
[tex]0.125*16 = 2[/tex]
2 planes fly from Dallas to Los Angeles
and 50% fly to St. Louis:
[tex]0.5*16 = 8[/tex]
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
[tex]20 - 6 + 8 = 22[/tex]
After 8 hours, there are 22 planes in Los Angeles.
St Louis:
Initially has 24 planes. 18 of them leave and 12 arrive. So
[tex]24 - 18 + 12 = 18[/tex]
After 8 hours, there are 18 planes in St. Louis
Dallas:
Initially has 16 planes. 10 of them leave, and 14 arrive. So:
[tex]16 - 10 + 14 = 20[/tex]
After 8 hours, there are 20 planes in Dallas.
