<p><img alt="$A$" height="14" src="https://latex.artofproblemsolving.com/0/1/9/019e9892786e493964e145e7c5cf7b700314e53b.png" width="15" /> and <img alt="$B$" height="14" src="https://latex.artofproblemsolving.com/f/f/5/ff5fb3d775862e2123b007eb4373ff6cc1a34d4e.png" width="17" /> move uniformly along two straight paths intersecting at right angles in point <img alt="$O$" height="14" src="https://latex.artofproblemsolving.com/5/1/d/51da37d984564162c87710ca27bea422f657fb73.png" width="16" />. When <img alt="$A$" height="14" src="https://latex.artofproblemsolving.com/0/1/9/019e9892786e493964e145e7c5cf7b700314e53b.png" width="15" /> is at <img alt="$O$" height="14" src="https://latex.artofproblemsolving.com/5/1/d/51da37d984564162c87710ca27bea422f657fb73.png" width="16" />, <img alt="$B$" height="14" src="https://latex.artofproblemsolving.com/f/f/5/ff5fb3d775862e2123b007eb4373ff6cc1a34d4e.png" width="17" /> is <img alt="$500$" height="14" src="https://latex.artofproblemsolving.com/a/3/9/a39b14023c98c943554d150561aacc188c4ce26d.png" width="29" /> yards short of <img alt="$O$" height="14" src="https://latex.artofproblemsolving.com/5/1/d/51da37d984564162c87710ca27bea422f657fb73.png" width="16" />. In two minutes they are equidistant from <img alt="$O$" height="14" src="https://latex.artofproblemsolving.com/5/1/d/51da37d984564162c87710ca27bea422f657fb73.png" width="16" />, and in <img alt="$8$" height="14" src="https://latex.artofproblemsolving.com/8/4/5/8455f3b5cb3b4880b8c9d782a5c1f0334db819eb.png" width="11" /> minutes more they are again equidistant from <img alt="$O$" height="14" src="https://latex.artofproblemsolving.com/5/1/d/51da37d984564162c87710ca27bea422f657fb73.png" width="16" />. Then the ratio of <img alt="$A$" height="14" src="https://latex.artofproblemsolving.com/0/1/9/019e9892786e493964e145e7c5cf7b700314e53b.png" width="15" />'s speed to <img alt="$B$" height="14" src="https://latex.artofproblemsolving.com/f/f/5/ff5fb3d775862e2123b007eb4373ff6cc1a34d4e.png" width="17" />'s speed is:</p> <p> </p>

Question No: 485

$A$ and $B$ move uniformly along two straight paths intersecting at right angles in point $O$ . When $A$ is at $O$ , $B$ is $500$ yards short of $O$ . In two minutes they are equidistant from $O$ , and in $8$ minutes more they are again equidistant from $O$ . Then the ratio of $A$ 's speed to $B$ 's speed is:

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Tags: Algebra

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