AMC 8 Daily Practice Round 8

Complete problem set with solutions and individual problem pages

Problem 18 Hard

Henry and Lesie are practicing shuttle runs between points A and B on the playground. Henry runs at a speed of 8 meters per second, and Lesie runs at 5 meters per second. They start at the same time from point A, run to point B, and then return. It is known that at their second head-on meeting, the meeting point is 5 meters away from the midpoint of AB. What is the distance between A and B in meters?

  • A.

    140

  • B.

    150

  • C.

    125

  • D.

    130

  • E.

    135

Answer:D

At their second head-on meeting, the two have together run a total of 4 full lengths.

Their speed ratio is 8:5, so Henry has run 4 \times \frac{8}{13} = \frac{32}{13} = 2\frac{6}{13} \ \text{(lengths)}.

The full length is 5 \div \left( \frac{1}{2} - \frac{6}{13} \right) = 130 \ \text{meters}.

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