AHSME 1970 Problem 32

$A$ and $B$ travel around a circular track at uniform speeds in opposite directions, starting from diametrically opposite points. If they start at the same time, meet first after $B$ has travelled $100$ yards, and meet a second time $60$ yards before $A$ completes one lap, then the circumference of the track in yards is $\text{(A) } 400 \text{(B) } 440 \text{(C) } 480 \text{(D) } 560 \text{(E) } 880$