MathDB
Who runs around a circular track anyway?

Source: AMC 10 2006A, Problem 15

February 6, 2006
AMC

Problem Statement

Odell and Kershaw run for 30 minutes on a circular track. Odell runs clockwise at 250 m/min and uses the inner lane with a radius of 50 meters. Kershaw runs counterclockwise at 300 m/min and uses the outer lane with a radius of 60 meters, starting on the same radial line as Odell. How many times after the start do they pass each other? <spanclass=latexbold>(A)</span>29<spanclass=latexbold>(B)</span>42<spanclass=latexbold>(C)</span>45<spanclass=latexbold>(D)</span>47<spanclass=latexbold>(E)</span>50 <span class='latex-bold'>(A) </span> 29 \qquad <span class='latex-bold'>(B) </span> 42 \qquad <span class='latex-bold'>(C) </span> 45 \qquad <span class='latex-bold'>(D) </span> 47 \qquad <span class='latex-bold'>(E) </span> 50