SOLUTION: I don't know why I can't figure these out. Given Running speed 12 km/hr and Biking 30 km/hr. It is a run, bike , then run. A duathlon consists of run, a bike ride and a sec

Question 498275: I don't know why I can't figure these out.
Given Running speed 12 km/hr and Biking 30 km/hr. It is a run, bike , then run.
A duathlon consists of run, a bike ride and a second run. Use the information below about the average rate of speed of a participant who completed a 55 kilometer duathlon in 2 hours and 25 minutes.
Write an equation based on the model. Solve the equation to find the time they spent running and the time they spent biking. Verify that their sum is 55 kilometers.
THanks again!!!
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = total running distance in km
Let = biking distance in km
given:
(1) km
= time for running
= time for biking
(2) hrs
-----------------------
The average speed is always ( total distance ) / (total time ), so

km/hr average speed
---------------
Multiply both sides of (2) by
(2)
Multiply both sides of (1) by
and subtract (1) from (2)
(2)
(1)

and, since

= time for running
= .9722 hrs
or 58 min 20 sec
= time for biking
= 1.4444 hrs
or 1 hr 26 min 40 sec
( the times add up to 2 hrs 25 min )
The key was that they never asked for the
separate distances for the 2 runs.
RELATED QUESTIONS
If I run my first 60 km lap at a rate 25% faster than my usual 12 km/hr, and my second 60 (answered by Theo)

if you bike a distance of 10 km at 30 km/hr, and then return at 20 km/hr, what is the... (answered by josgarithmetic)

Hi. I hope that you can help me. I have talked to others in my class, and we are all... (answered by scott8148)

At 10:30am two planes leave Houston, one flying east at 560 km/h and the other west at... (answered by mananth,MathTherapy)

Stanley practices his running, swimming and biking every day. During these practices he... (answered by MathTherapy,Edwin McCravy,ikleyn,mccravyedwin)

an express train makes a run of 240 km at acertain speed. Another train whose speed is 12 (answered by josmiceli,ankor@dixie-net.com)

In a 16 km cross-country ski race Brett skied the first 7 km at a constant speed and then (answered by jorel1380)

Hello I have a uniform motion problem involving rational expressions, I normally get... (answered by Theo)

If a boat is moving in upstream with velocity of 14 km/hr and goes downstream with a... (answered by dabanfield)