1950 AHSME Problems/Problem 50
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[hide]Problem
A privateer discovers a merchantman miles to leeward at 11:45 a.m. and with a good breeze bears down upon her at mph, while the merchantman can only make mph in her attempt to escape. After a two hour chase, the top sail of the privateer is carried away; she can now make only miles while the merchantman makes . The privateer will overtake the merchantman at:
Solution
Assume that the two boats are traveling along the positive real number line, with the merchantman starting at the number and the privateer starting at the number . After two hours the merchantman is at while the privateer is at . When the top sail of the privateer is carried away, the speed of the merchantman is unaffected; he still travels at miles per hour. Therefore the privateer travels at miles per hour. The remaining time in hours it takes for the privateer to catch up to the merchantman satisfied the equation
Simplification yields the equation , which shows that . It therefore takes a total of hours for the privateer to catch the merchantman, so this will happen at
Video Solution
https://www.youtube.com/watch?v=l4lAvs2P_YA&t=437s
~MathProblemSolvingSkills.com
See Also
1950 AHSC (Problems • Answer Key • Resources) | ||
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