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2002 AMC 12A Problem 11

Problem 11 of 25IntermediateAlgebra

Mr. Earl E. Bird leaves his house for work at exactly 8:008{:}00 A.M. every morning. When he averages 4040 miles per hour, he arrives at his workplace three minutes late. When he averages 6060 miles per hour, he arrives three minutes early. At what average speed, in miles per hour, should Mr. Bird drive to arrive at his workplace precisely on time?

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Solution

Let tt be the time in hours to arrive on time. Since three minutes is 0.050.05 hours, 40(t+0.05)=60(t0.05).40(t+0.05) = 60(t-0.05). This gives 40t+2=60t3,40t + 2 = 60t - 3, so t=0.25.t = 0.25. The distance is 40(0.25+0.05)=1240(0.25+0.05) = 12 miles, and the required speed is 120.25=48\dfrac{12}{0.25} = 48 miles per hour. Thus, the correct answer is B.

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Concepts: distance rate and time · system of equations

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.