Question 929217: during the first part of a trip a canoeist travels 24 miles at a certain speed. The canoeist travels 7 miles on the second part of the trip at a speed 5 miles per hour slower. The total time for the trip is 3 hours . What was the speed for each part of the trip?
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! x = speed first part
y = speed second part = x - 5
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s = d/t
t = d/s
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first part:
a = 24/x
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second part:
t = 7/y
b = 7/(x - 5)
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a + b = 3
24/x + 7/(x - 5) = 3
24(x - 5)/x(x - 5) + 7x/x(x - 5) = 3
24(x - 5) + 7x = 3x(x - 5)
24x - 5*24 + 7x = 3xx - 15x
24x - 120 + 7x = 3xx - 15x
3xx - 15x - 24x - 7x + 120 = 0
3xx - 46x + 120 = 0
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the above quadratic equation is in standard form, with a=3, b=-46 and c=120
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to solve the quadratic equation, by using the quadratic formula, copy and paste this:
3 -46 120
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the quadratic has two real roots at:
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x = 12
x = 3.33333333
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the root x=3.333 doesn't fit the problem statement, because (y=3.333 - 5) and y becomes negative, so use the root x=12:
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x = 12
y = x - 5
y = 12 - 5
y = 7
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answer:
x = speed first part = 12 mph
y = speed second part = 7 mph
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