MathDB
Speeds and distances

Source: AHSME 1991 problem 11

October 16, 2011
AMC

Problem Statement

Jack and Jill run 1010 kilometers. They start at the same point, run 55 kilometers up a hill, and return to the starting point by the same route. Jack has a 1010 minute head start and runs at the rate of 1515 km/hr uphill and 2020 km/hr downhill. Jill runs 1616 km/hr uphill and 2222 km/hr downhill. How far from the top of the hill are they when they pass going in opposite directions?
<spanclass=latexbold>(A)</span> 54 km<spanclass=latexbold>(B)</span> 3527 km<spanclass=latexbold>(C)</span> 2720 km<spanclass=latexbold>(D)</span> 73 km<spanclass=latexbold>(E)</span> 289 km <span class='latex-bold'>(A)</span>\ \frac{5}{4}\ km\qquad<span class='latex-bold'>(B)</span>\ \frac{35}{27}\ km\qquad<span class='latex-bold'>(C)</span>\ \frac{27}{20}\ km\qquad<span class='latex-bold'>(D)</span>\ \frac{7}{3}\ km\qquad<span class='latex-bold'>(E)</span>\ \frac{28}{9}\ km