Question 208716
In a three-person, 100-meter race,Amy finishes 10 meters ahead of Brooke and 20 meters ahead of Carol. 
Assuming constant speeds for each runner, by how many meters did Brooke finish ahead of Carol?
:
Let t = A's time to run 100 meters
then
During this time; B ran 90m and C ran 80m
:
Find their speed: speed = Dist/time
:
{{{90/t}}} = B's speed
and
{{{80/t}}} = C's speed
:
Find B's time to run 100 yds (time = dist/speed)
B's time = {{{100/(90/t)}}} = 100 * {{{t/90)}}} = {{{(100t)/90}}} = {{{(10t)/9}}}
Find how far C runs in {{{(10t)/9}}}; (Dist = speed * time)
C's dist = {{{80/t}}} * {{{(10t)/9}}}
Cancel t:
80*{{{(10)/9}}} = {{{800/9}}} = 88.89 ft
therefore
100 - 88.89 = 11.11 meters; C is behind when B crosses the finish line
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Hope this makes sense to you?