1961 AHSME Problems/Problem 37
Contents
Problem
In racing over a distance at uniform speed, can beat by yards, can beat by yards, and can beat by yards. Then , in yards, equals:
Solution
Let be speed of , be speed of , and be speed of .
Person finished the track in minutes, so traveled yards at the same time. Since is yards from the finish line, the first equation is Using similar steps, the second and third equation are, respectively, Get rid of the denominator in all three equations by multiplying both sides by the denominator in each equation. These equations can be rearranged to get the following.
Solving for in the first equation yields . Substituting for and solving for in the second equation yields . Substituting for in the third equation yields Solve the equation to get . Thus, the track is yards long, which is answer choice .
Solution 2
Let , , be the speeds of , , , respectively and let , , be their respective times needed, such that Putting each pair of them into a race gets the equations Subtract the first equation from the third yields Divide the equation by the second original equation yields Since we have Thus from the first equation we have
~ Nafer
See Also
1961 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 36 |
Followed by Problem 38 | |
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