Run around the track!

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Anastasia runs at a steady speed of 12 miles per hour, while Kristina runs at a steady speed of 10 miles per hour. They both start at the same spot on a circular track 1 4 -mile long and run in opposite directions. How many miles will Anastasia have run when they meet for the 30th time? Express your answer as a mixed number.

3 1/11 4 1/11 Not enough Information 4/11

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Shawn Ong
May 8, 2015

Since they run in opposite directions, we can simply consider the sum of their speeds as 22 miles per hour. Every time they meet, they combine for a full lap, so we want 30 laps.

$30 \times \frac {1}{4} = \frac {15}{2}$

For every 22 miles the pair runs, Anastasia runs 12. So we take $\frac {15}{2} \times \frac {12}{22} = \frac {45}{11} = \boxed {4 \frac{1}{11}}$

Run around the track!

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