13. A rabbit and a hedgehog participated in a running race on a $550 \mathrm{~m}$ long circular track, both starting and finishing at the same point. The rabbit ran clockwise at a speed of $10 \mathrm{~m} / \mathrm{s}$ and the hedgehog ran anticlockwise at a speed of $1 \mathrm{~m} / \mathrm{s}$. When they met, the rabbit continued as before, but the hedgehog turned round and ran clockwise. How many seconds after the rabbit did the hedgehog reach the finish?
SOLUTION
B

Initially their relative speed, in $\mathrm{m} / \mathrm{s}$, is $10+1=11$, so the time in seconds which elapses before they meet is $550 \div 11=50$ seconds. The hedgehog takes 50 seconds to get back again, and the rabbit covers the same distance in one-tenth of the time ( 5 seconds). Hence a difference of 45 seconds.