SOLUTION: In a five mile race betty was 1/4 of a mile back when Ann crossed the finish line and Cindy was 1/3 of a mile back when Betty finished. Assuming that all three maintained their sam

Question 874131: In a five mile race betty was 1/4 of a mile back when Ann crossed the finish line and Cindy was 1/3 of a mile back when Betty finished. Assuming that all three maintained their same pace throughout the race how far back was Cindy when Ann finished the race?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
ONE WAY TO DO IT:
In the time that Ann ran miles,
Betty only covered miles.
Betty is slower than Ann.
Compared to Ann's speed, Betty's speed is
of Ann's speed.
Betty's speed is of Ann's speed.

In the time that Betty ran miles,
Cindy only covered miles.
Cindy is slower than Betty .
Compared to Betty's speed, Cindy's speed is
of Betty's speed.
Cindy's speed is of Betty's speed.

Compared to Ann's speed, Cindy's speed is
of of Ann's speed, or
of Ann's speed.
So, in the time that Ann ran miles,
Cindy covered miles.
That means that when Ann finished the race,
Cindy had only ran out of the miles.
So Cindy was
miles back.

ANOTHER WAY:
We could say that Ann ran the 5 miles in minutes, and then we can calculate Ann's, Betty's and Cindy"s speeds in miles per minute based on that:
= Ann's speed.
Since Betty was mile back,
and had only covered miles in that time ,
= Betty's speed.
So Betty would take minutes to finish.
In that time, Cindy had only ran miles,
so Cindy's speed, in miles per minute, is
.
That means that, in the time that it took for Ann to finish the race,
Cindy had covered miles.
So, to get to the finish line, Cindy still had to run
miles back.

SIMPLER:
We can set an arbitrary time.
Let's say that Ann's time was 40 minutes.
Ann ran at miles per minute.
Betty had ran miles in those 40 minutes.
Betty ran at miles per minute.
At that speed it would take her
minutes to finish the 5 mile race.
In that time, Cindy had only run miles.
Cindy's speed was about miles per minute.
At that speed, in the 40 minutes that it took Ann to finish the race,
Cindy covered approximately miles,
and at that point she was about
miles back.
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