Question

如图，P是定长线段AB上一点，C、D两点分别从P、B出发以1cm/s、2 cm/s的速度沿直线AB向左运动

（C在线段AP上，D在线段BP上）
1.设AB=30cm，当C,D运动时间为1S时，有pd=2ac求AP长
2、设AB=30cm，当C,D运动时间为2S时，有pd=2ac求AP长
3设AB=30cm，当C,D运动到任意时刻时，有pd=2ac求AP长

Answer 1

AB=30cm，当C,D运动时间为1S时，
PC = 1*1 = 1
BD = 2*1 = 2
AC = AP-PC = AP-1
PD = PB-BD = PB-AP-BD = 30-AP-2 = 28-AP
PD = 2AC
28-AP = 2(AP-1)
3AP = 30
AP = 10

AB=30cm，当C,D运动时间为1S时，
PC = 1*2 = 2
BD = 2*2 = 4
AC = AP-PC = AP-2
PD = PB-BD = PB-AP-BD = 30-AP-4 = 26-AP
PD = 2AC
26-AP = 2(AP-2)
3AP = 30
AP = 10 cm

AB=30cm，当C,D运动时间为1S时，
PC = 1*1 = 1
BD = 2*1 = 2
AC = AP-PC = AP-1
PD = PB-BD = PB-AP-BD = 30-AP-2 = 28-AP
PD = 2AC
28-AP = 2(AP-1)
3AP = 30
AP = 10

AB=30cm，当C,D运动时间为任意时间t时，
PC = 1*t = t
BD = 2*t = 2t
AC = AP-PC = AP-t
PD = PB-BD = PB-AP-BD = 30-AP-2t
PD = 2AC
30-AP-2t = 2(AP-t)
3AP = 30
AP = 10 cm