Algebra
posted by Terri .
Jan and Carol are competing in the 500m Freestyle swimming competition. In this event, swimmers make 10 laps in a 50 meter pool. Carol finished the race in 2 minutes, 40 seconds and swam 1/4 m per second faster than Jan. What was Jan's time?

Let j be Jan's time.
Use the formula d = r * t (distance = rate times time). 
still lost

Interesting result
I used to coach swimming and have never heard of a 500 m race.
There is a 400 m and a 800 m freestyle.
As of Dec 3/07 the world record in the 400 m men's freestyle was still held by
Ian Thorpe, AUS in a time of 3:40.08
So Carol did 500 m in 2:40 !!! WOW
Be that as it may, ...
Carol swam 500 m in 160 seconds, so she swam at a rate of 500/160 m/sec or 3.125 m/sec.
So Jan swam 1/4 or .124 m/sec slower, so she swam at 3 m/sec
time = dist/rate
= 500/3 sec
= 166.667 sec
= 2 min, 47 sec (2:47) 
I understand the 3.125 m/sec, but I am not sure how you got .124 m/sec

My error Terri, 1/4 of course is .25 not .124
so let's pick it up at..
So Jan swam 1/4 or ..25 m/sec slower, so she swam at 2.875 m/sec (3.125 .25)
time = dist/rate
= 500/2.875 sec
= 173.913 sec
= 2 min, 53.9 sec (2:53.9) 
Thanks for your help!