东西两镇距离s,甲,乙,丙三人速度j,y,b:
当甲与丙相遇时,乙距他们20km,s/(j+b)=(s-20km)/(y+b)=20km/(j-y)。。。。。(1)
当乙与丙相遇时,甲距他们30km,s/(y+b)=(s+30km)/(j+b)=30km/(j-y)。。。。。(2)
当甲到达西镇时,丙距东镇还有20km,s/j=(s-20km)/b。。。。。(3)
由(3)得s=20km/(1-b/j)
由(1)得s=(1+b/j)20km/(1-y/j),则y/j=(b/j)^2
由(2)得s=(y/j+b/j)30km/(1-y/j)=(b/j)30km/(1-b/j)=20km/(1-b/j),所以b/j=2/3,b=2j/3
所以s=60km,y/j=4/9,y=4j/9,y/b=2/3
那么当丙到达东镇时,乙距西镇多远?s-ys/b=60km-60km*2/3=20km