smc

Let $x$ be half the circumference of the track. They first meet after $B$ has run $100$ yards, meaning that in the time $B$ has run $100$ yards, $A$ has run $x-100$ yards. The second time they meet is when $A$ is 60 yards before he completes the lap. This means that in the time that $A$ has run $2x-60$ yards, $B$ has run $x+60$ yards. Because they run at uniform speeds, we can write the equation $$\frac{100}{x-100}=\frac{x+60}{2x-60}.$$ Cross multiplying, $$200x-6000=x^2-40x-6000$$ Adding $6000$ to both sides and simplifying, we have $$200x=x^2-40x$$ $$240x=x^2$$ $$x=240.$$ Because $x$ is only half of the circumference of the track, the answer we are looking for is $2\cdot 240=480,\text{or }\boxed{480}$.