SOLUTION: Janet is training for a triathlon. Yesterday she jogged for 12 miles and then cycled another 31.5 miles. Her speed while cycling was 6 miles per hour faster than while jogging. If

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Question 1072602: Janet is training for a triathlon. Yesterday she jogged for 12 miles and then cycled another 31.5 miles. Her speed while cycling was 6 miles per hour faster than while jogging. If the total time for jogging and cycling was 3.75 hours, at what rate did she cycle.
Answer by josgarithmetic(39614) About Me  (Show Source):
You can put this solution on YOUR website!
r, speed cycled
               SPEED       TIME           DISTANCE
JOG             r-6        12/(r-6)        12
CYCLE           r          31.5/r          31.5
Total                       3.75


12%2F%28r-6%29%2B31.5%2Fr=3.75

Multiply both sides by r%28r-6%29 and simplify......

r%5E2-17.6r%2B50.4=0
Discriminant, 10.4%5E2
.
Solutions found to the quadratic, system%28r=3.6%2COR%2Chighlight_green%28highlight_green%28r=14%29%29%29

Only the 14 mile per hour value is meaningful.