Question 934607: To train for the running of a triathlon, Jerri jogs 1 hour each day over the same 7 mile course. Four miles of the course is downhill, whereas the other 3 miles is on level ground. Jerri figures that she runs 2 miles per hour faster downhill than she runs on level ground. Find the rate at which Jerri runs on level ground.
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! x = speed on level ground
y = speed downhill
y = x + 2
t = time downhill
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s = d/t
t = d/s
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time downhill:
t = 4/y
t = 4/(x + 2)
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time on level ground:
1 - t = 3/x
t = 1 - 3/x
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equate times:
4/(x + 2) = 1 - 3/x
4/(x + 2) = x/x - 3/x
4/(x + 2) = (x - 3)/x
4x = (x - 3)(x + 2)
4x = xx + 2x - 3x - 6
xx - 5x - 6 = 0
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the above quadratic equation is in standard form, with a=1, b=-5 and c=-6
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1 -5 -6
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the quadratic has two real roots at:
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x = 6
x = -1
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the negative root doesn't fit the problem statement, so use the positive root:
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answer:
x = speed on level ground = 6 mph
y = speed downhill = 8 mph
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