SOLUTION: Competing in a mini-triathlon, Catherine ran 3 miles in the same amount of time she biked 12 miles. Her average speed on the bike was 18 mph more than her average running speed. Wh

Algebra ->  Finance -> SOLUTION: Competing in a mini-triathlon, Catherine ran 3 miles in the same amount of time she biked 12 miles. Her average speed on the bike was 18 mph more than her average running speed. Wh      Log On


   

Question 1088680: Competing in a mini-triathlon, Catherine ran 3 miles in the same amount of time she biked 12 miles. Her average speed on the bike was 18 mph more than her average running speed. What was her running speed?
Answer by ikleyn(52785) About Me  (Show Source):
You can put this solution on YOUR website!
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Let r be her running speed, in miles per hour.

Then her biking speed is (r+18) mph.


The time of running 3 miles was 3%2Fr hours. (= distance/rate)

The time of biking was 12%2F%28r%2B18%29 hours.    (= distance/rate)


The condition says that 

3%2Fr = 12%2F%28r%2B18%29.


It is your equation. You must solve it to find the unknown r.


I can solve it mentally: r = 6 mph.


If you want to solve it analytically, then multiply both sides by r*(r+18); then simplify. You will get a quadratic equation.


Solve it by factoring or use the quadratic formula.


You just know the answer.