1964 AHSME Problems/Problem 26
Problem
In a ten-mile race beats by miles and beats by miles. If the runners maintain constant speeds throughout the race, by how many miles does beat ?
Solution
Let the speeds of the runners in miles per hour be , with . If person reaches the finish line in hours, then we have .
Thus, the speeds of the second and third place people are and . The ratio of those speeds is , meaning person runs times as fast as person , or conversely that person is times slower than person .
If runs times as fast as , then when has finished the race at miles, will run miles. This is a difference of miles, which is answer
See Also
1964 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 25 |
Followed by Problem 27 | |
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