No.135 Moving Around a Circular Path
Example
A circular park has a perimeter of 2,400 m. A rides a bicycle and B walks. Starting at the same point at the same time in opposite directions, they first meet after 8 minutes. Starting in the same direction, A first catches B after 12 minutes. Find each speed in meters per minute.
POINT
Let x and y be A’s and B’s speeds (m/min). Opposite directions: in 8 minutes their combined distance is one lap, so 8(x+y)=2400. Same direction: in 12 minutes A gains one lap on B, so 12(x−y)=2400. Solve these two equations.
A：毎分250 m、B：毎分50 m
TRY
TRY 1
A circular path has a perimeter of 1,800 m. Traveling in opposite directions, A and B meet after 6 minutes; traveling in the same direction, A catches B after 9 minutes. Find their speeds in meters per minute.
A: 250 m/min; B: 50 m/min
TRY 2
A circular path has a perimeter of 1,200 m. Traveling in opposite directions, A and B meet after 5 minutes; traveling in the same direction, A catches B after 10 minutes. Find their speeds in meters per minute.
A: 180 m/min; B: 60 m/min