Question 704249: Maureen can run at a rate that is 3 miles per hour faster than her friend Hector's rate. While training for a mini marathon, Maureen gives Hector a half-hour head start and then begins chasing Hector on the same route. If Maureen passes Hector 9 miles from the starting point, how fast is each running?
Answer by josgarithmetic(39613)   (Show Source):
You can put this solution on YOUR website! Trying to put this into a rate-time-distance chart seemed confusing, but they both are at the same distance, 9 miles, when She catchs-up; meanwhile Hector has already gone  miles. Let t be the time needed for Maureen to match Hector's distance of 9 miles. Let Hector's speed be r.
When she passes Hector:
Maureen, 
Hector, 
Yes, during catchup time, Hector traveled less than 9 miles; the "t" is for catchup time.
Each equation transformable to solve for t.
Maureen: 
Hector: 
Equate the time, t:
.
with a bit of work,
.
Solution to quadratic formula,,...
 miles per hour. That's Hector's speed.
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