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2004 AMC 10A Problem 17

Problem 17 of 25IntermediateAlgebra

Brenda and Sally run in opposite directions on a circular track, starting at diametrically opposite points. They first meet after Brenda has run 100100 meters. They next meet after Sally has run 150150 meters past their first meeting point. Each girl runs at a constant speed. What is the length of the track in meters?

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Solution

Before the first meeting the two together cover half the track. Between the first and second meetings they together cover a full track, which is twice as far, so Brenda runs 2100=2002 \cdot 100 = 200 meters in that stretch. Sally runs 150150 meters in the same stretch, so the full track length is 200+150=350. 200 + 150 = 350. Thus, the correct answer is C.

More practice

Concepts: relative speed · distance rate and time · ratio and proportion

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