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A and B running around a track

Source: 1959 AHSME Problem 30

August 14, 2013
AMCalgebraAMC 12

Problem Statement

AA can run around a circular track in 4040 seconds. BB, running in the opposite direction, meets AA every 1515 seconds. What is BB's time to run around the track, expressed in seconds? <spanclass=′latex−bold′>(A)</span> 1212<spanclass=′latex−bold′>(B)</span> 24<spanclass=′latex−bold′>(C)</span> 25<spanclass=′latex−bold′>(D)</span> 2712<spanclass=′latex−bold′>(E)</span> 55 <span class='latex-bold'>(A)</span>\ 12\frac12 \qquad<span class='latex-bold'>(B)</span>\ 24\qquad<span class='latex-bold'>(C)</span>\ 25\qquad<span class='latex-bold'>(D)</span>\ 27\frac12\qquad<span class='latex-bold'>(E)</span>\ 55
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