1968 AHSME Problems/Problem 32
Problem
and move uniformly along two straight paths intersecting at right angles in point . When is at , is yards short of . In two minutes they are equidistant from , and in minutes more they are again equidistant from . Then the ratio of 's speed to 's speed is:
Solution
Let the speed of be and the speed of be . The first time that and will be equidistant from , will have not yet reached . Thus, after two minutes, 's distance from will be , and 's distance from will be . Setting these expressions equal to each other and dividing by 2, we see that .
After another eight minutes (or after a total of ten minutes since was at ), and will again be equidistant from , but this time will have passed . The distance will be from is , and the distance will be from is . Setting these expressions equal to each other and dividing by 10, we see that .
Adding the two equations that we have obtained above, we see that , and so . Substituting this value of into the second equation, we see that , or . Then, , so the ratio of 's speed to that of is .
See also
1968 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 31 |
Followed by Problem 33 | |
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