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

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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) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = total running distance in km
Let b = biking distance in km
given:
(1) +a+%2B+b+=+55+ km
+a%2F12+ = time for running
+b%2F30+ = time for biking
(2) +a%2F12+%2B+b%2F30+=+29%2F12+ hrs
-----------------------
The average speed is always ( total distance ) / (total time ), so
+55+%2F+%285%2F12%29+=+%2812%2F5%29%2A55+
+12%2A11+=+132+ km/hr average speed
---------------
Multiply both sides of (2) by 60
(2) +5a+%2B+2b+=+145+
Multiply both sides of (1) by +2+
and subtract (1) from (2)
(2) +5a+%2B+2b+=+145+
(1) +-2a+-+2b+=+110+
+3a+=+35+
+a+=+35%2F3+
and, since
+a+%2B+b+=+55+
+b+=+165%2F3+-+35%2F3+
+b+=+130%2F3+
+a%2F12+ = time for running
+%2835%2F3%29%2A%281%2F12%29+ = .9722 hrs
or 58 min 20 sec
+b%2F30+ = time for biking
+%28130%2F3%29%2A%281%2F30%29+ = 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.