MathDB

6

Part of 2008 AMC 10

Problems(2)

Triathlon

Source: AMC 10 2008A Problem 6

2/22/2008
A triathlete competes in a triathlon in which the swimming, biking, and running segments are all of the same length. The triathlete swims at a rate of 3 3 kilometers per hour, bikes at a rate of 20 20 kilometers per hour, and runs at a rate of 10 10 kilometers per hour. Which of the following is closest to the triathlete's average speed, in kilometers per hour, for the entire race? <spanclass=latexbold>(A)</span> 3<spanclass=latexbold>(B)</span> 4<spanclass=latexbold>(C)</span> 5<spanclass=latexbold>(D)</span> 6<spanclass=latexbold>(E)</span> 7 <span class='latex-bold'>(A)</span>\ 3 \qquad <span class='latex-bold'>(B)</span>\ 4 \qquad <span class='latex-bold'>(C)</span>\ 5 \qquad <span class='latex-bold'>(D)</span>\ 6 \qquad <span class='latex-bold'>(E)</span>\ 7
AMC
Segment Ratios

Source: AMC 12 2008B Problem 8

2/29/2008
Points B B and C C lie on AD \overline{AD}. The length of AB \overline{AB} is 4 4 times the length of BD \overline{BD}, and the length of AC \overline{AC} is 9 9 times the length of CD \overline{CD}. The length of BC \overline{BC} is what fraction of the length of AD \overline{AD}? <spanclass=latexbold>(A)</span> 136<spanclass=latexbold>(B)</span> 113<spanclass=latexbold>(C)</span> 110<spanclass=latexbold>(D)</span> 536<spanclass=latexbold>(E)</span> 15 <span class='latex-bold'>(A)</span>\ \frac{1}{36} \qquad <span class='latex-bold'>(B)</span>\ \frac{1}{13} \qquad <span class='latex-bold'>(C)</span>\ \frac{1}{10} \qquad <span class='latex-bold'>(D)</span>\ \frac{5}{36} \qquad <span class='latex-bold'>(E)</span>\ \frac{1}{5}
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