2008/09 AHSMC Part 1 Problem 10

Problem 10 of 16

Linda is walking at constant speed halfway between two parallel train tracks. On each track is a train of the same length. They are approaching Linda from different directions, both at $V$ kilometres per hour. The one going the same way as Linda takes $t_1$ seconds to pass her, while the other takes $t_2$ seconds to pass her. In kilometres per hour, Linda's walking speed is

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Let Linda's walking speed be $v$ kilometres per hour. Then the length of the trains is given by $t_1(V - v) = t_2(V + v)$ . It follows that $v = \dfrac{t_1-t_2}{t_1+t_2}V$ . The answer is (A).

University of Alberta

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