question: Piecewise functions $f$ and $g$ can model the heights (in meters) of two airplanes. $g$ is purple and goes through (0,10000), (40,9000), (80,9000), (100,11000), (130,11000), and $f$ is blue and goes through (10,11000), (50,11000), (60,10000), (100,10000), (120,0). $t$ is the number of minutes that have passed since noon at a local airport. Which statements represent the meaning of the intersection points of the graphs?
  Choices:
  A.They mean that one airplane was initially higher than the other airplane.
  B.They mean that the airplanes reached the same height when they were both at 10,000 meters.
  C.They give the solutions to the equation $f(t)=0$.
  D.They give the solutions to the equation $f(t)=g(t)$.
query_wo: Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.
  Question: Piecewise functions $f$ and $g$ can model the heights (in meters) of two airplanes. $g$ is purple and goes through (0,10000), (40,9000), (80,9000), (100,11000), (130,11000), and $f$ is blue and goes through (10,11000), (50,11000), (60,10000), (100,10000), (120,0). $t$ is the number of minutes that have passed since noon at a local airport. Which statements represent the meaning of the intersection points of the graphs?
  Choices:
  A.They mean that one airplane was initially higher than the other airplane.
  B.They mean that the airplanes reached the same height when they were both at 10,000 meters.
  C.They give the solutions to the equation $f(t)=0$.
  D.They give the solutions to the equation $f(t)=g(t)$.
query_cot: Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
  Question: Piecewise functions $f$ and $g$ can model the heights (in meters) of two airplanes. $g$ is purple and goes through (0,10000), (40,9000), (80,9000), (100,11000), (130,11000), and $f$ is blue and goes through (10,11000), (50,11000), (60,10000), (100,10000), (120,0). $t$ is the number of minutes that have passed since noon at a local airport. Which statements represent the meaning of the intersection points of the graphs?
  Choices:
  A.They mean that one airplane was initially higher than the other airplane.
  B.They mean that the airplanes reached the same height when they were both at 10,000 meters.
  C.They give the solutions to the equation $f(t)=0$.
  D.They give the solutions to the equation $f(t)=g(t)$.
question_for_eval: Piecewise functions $f$ and $g$ can model the heights (in meters) of two airplanes. $g$ is purple and goes through (0,10000), (40,9000), (80,9000), (100,11000), (130,11000), and $f$ is blue and goes through (10,11000), (50,11000), (60,10000), (100,10000), (120,0). $t$ is the number of minutes that have passed since noon at a local airport. Which statements represent the meaning of the intersection points of the graphs?
  Choices:
  A.They mean that one airplane was initially higher than the other airplane.
  B.They mean that the airplanes reached the same height when they were both at 10,000 meters.
  C.They give the solutions to the equation $f(t)=0$.
  D.They give the solutions to the equation $f(t)=g(t)$.