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 $\frac[3}{4}$ (Error compiling LaTeX. Unknown error_msg) 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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