2011/12 AHSMC Part 1 Problem 10

Problem 10 of 16

The perimeter of a square lawn consists of four straight paths. Annabel and Bethany started at the same corner at the same time, running clockwise at constant speeds of $12$ and $10$ kilometres per hour respectively. Annabel finished one lap around the lawn in $1$ minute. During this minute, the number of seconds that Annabel and Bethany were on the same path is

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Solution

Annabel spent $15$ seconds on each path, and Bethany $18$ seconds. On the first path, Bethany was with Annabel all $15$ seconds. On the second path, Bethany joined Annabel $3$ seconds late, and was with her for $12$ seconds. On the third path, Bethany was with Annabel for $9$ seconds. On the fourth path, Bethany was with Annabel for $6$ seconds. The total is $15+12+9+6=42$ seconds. The answer is (B).

University of Alberta

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