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

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(52786) (Show Source): You can put this solution on YOUR website!
.

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  hours. (= distance/rate)

The time of biking was  hours.    (= distance/rate)


The condition says that 

 = .


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.

RELATED QUESTIONS
In a special triathlon, Betty swam 2 miles in 25 minutes, biked 30 miles in 45... (answered by checkley79)

Dan competed in a triathlon that covered 46.5 miles. He began by swimming at an average... (answered by ankor@dixie-net.com)

Yesterday, Linda went on a bike ride. He average speed was 9MPH. Today, she went on... (answered by addingup)

Jill was training for a triathlon, so she planned a day of exercising. She spent a total... (answered by josgarithmetic)

Mar T. Ello participated in a triathlon in which he swam 3 miles, ran 5 miles and then... (answered by Edwin McCravy)

Karin can run 3 miles per hour faster than her sister Kim can walk. If Karin ran 12 miles (answered by ikleyn,greenestamps)

two cyclists are competing in a 12 miles race on a quarter mile circular track. They... (answered by checkley77)

In a triathlon, Jenny swim for one hour, bike for 1.75 hours, and ran for one hour. Her... (answered by josgarithmetic,MathTherapy,ikleyn)

I have a word problem that I cannot get into the right form. If I can get it into the... (answered by rwm)