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Michael and the Garbage Truck

Source: AMC 12 2008B Problem 20

February 28, 2008
ratioAMC

Problem Statement

Michael walks at the rate of 5 5 feet per second on a long straight path. Trash pails are located every 200 200 feet along the path. A garbage truck travels at 10 10 feet per second in the same direction as Michael and stops for 30 30 seconds at each pail. As Michael passes a pail, he notices the truck ahead of him just leaving the next pail. How many times will Michael and the truck meet? <spanclass=latexbold>(A)</span> 4<spanclass=latexbold>(B)</span> 5<spanclass=latexbold>(C)</span> 6<spanclass=latexbold>(D)</span> 7<spanclass=latexbold>(E)</span> 8 <span class='latex-bold'>(A)</span>\ 4\qquad <span class='latex-bold'>(B)</span>\ 5\qquad <span class='latex-bold'>(C)</span>\ 6\qquad <span class='latex-bold'>(D)</span>\ 7\qquad <span class='latex-bold'>(E)</span>\ 8