Question 931271: Audrey drove her empty truck 300 miles to Salinas to pick up a load of sweet potatoes. when her truck was fully loaded, her average speed was 10 miles per hour less than when her truck was empty. If the return trip took 1 hour longer, then what was her average speed with the truck empty?
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! x = speed with truck empty
y = speed with truck full = x - 10
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z = time with truck empty
w = time with truck full = z + 1
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s = d/t
t = d/s
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time with truck empty:
z = 300/x
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time with truck full:
w = 300/y
z + 1 = 300/(x - 10)
z = 300/(x - 10) - 1
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equate z's:
300/x = 300/(x - 10) - 1
300/x - 300/(x - 10) = -1
300(x - 10)/x(x - 10) - 300x/x(x - 10) = -1
300(x - 10) - 300x = -x(x - 10)
300x - 3000 - 300x = -xx + 10x
-3000 = -xx + 10x
xx - 10x - 3000 = 0
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the above quadratic equation is in standard form, with a=1, b=-10 and c=-3000
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to solve the quadratic equation, by using the quadratic formula, copy and paste this:
1 -10 -3000
into this solver: https://sooeet.com/math/quadratic-equation-solver.php
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the quadratic has two real roots at:
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x = 60
x = -50
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the negative root doesn't fit the problem statement, so use the positive root:
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x = 60
y = x - 10
y = 50
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answer:
x = speed with truck empty = 60 mph
y = speed with truck full = 50 mph
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