Question 819277: Need help setting up the equation
Tina is training for a biathlon. To train for the running portion of the race, she runs 10 miles each day, over the same course. The first 4 miles of the course is on level ground, while the last 6 miles is downhill. She runs 4 miles per hour slower on level ground than she runs downhill. If the complete course takes 1 hour, how fast does she run on the downhill part of the course?
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! s = d / t
t = d / s
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level time:
t = 4/s
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downhill time:
t = 6/(s + 4)
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total time:
4/s + 6/(s + 4) = 1
4(s + 4)/s(s + 4) + 6s/s(s + 4) = 1
4(s + 4) + 6s = s(s + 4)
4s + 16 + 6s = ss + 4s
ss - 6s - 16 = 0
s^2 - 6s - 16 = 0
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the above quadratic equation is in standard form, with a=1, b=-6, and c=-16
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to solve the quadratic equation, plug this:
1 -6 -16
into this: https://sooeet.com/math/quadratic-equation-solver.php
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the quadratic roots are:
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s = 8
s = -2
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the negative root doesn't make sense for speed in this problem, so use the positive root
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speed on flat ground = 8 mph
speed downhill = 12 mph
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