1970 AMC 12 Problem 32

Let the circumference be $2C$ and compare the two runners’ traveled-distance ratios at each meeting

At the first meeting their distances are $C-100$ and $100$; at the second they are $2C-60$ and $C+60$

Let the circumference be $2C.$ At the first meeting, $B$ has traveled $100$ yards and $A$ has traveled $C-100,$ so their speed ratio is $$\frac{v_A}{v_B}=\frac{C-100}{100}.$$ At the second meeting, $A$ is $60$ yards short of one lap, so it has traveled $2C-60.$ By then their combined distance is $3C,$ so $B$ has traveled $C+60.$ Hence $$\frac{C-100}{100}=\frac{2C-60}{C+60}.$$ Cross-multiplying gives $C=240,$ so the circumference is $2C=480$ yards.

Therefore, the correct answer is C.