Question 934762: Using one engine of a ferry boat, it takes 6 h longer to cross a channel than it does using a second engine alone. with both engines operating, the ferryboat can make the crossing in 4 h. how long would it take each engine, working alone, to power the ferry boat across the channel?
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! x = time for engine A alone
y = time for engine B alone
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y = x + 6
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r = w/t
rates are additive:
1/x + 1/y = 1/4
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1/x + 1/y = 1/4
1/x + 1/(x + 6) = 1/4
1(x + 6)/x(x + 6) + 1x/x(x + 6) = 1/4
1(x + 6) + 1x = (1/4)x(x + 6)
x + 6 + x = (1/4)xx + (6/4)x
(1/4)xx + (6/4)x - 2x - 6 = 0
(1/4)xx + (6/4)x - (8/4)x - 6 = 0
(1/4)xx - (2/4)x - 6 = 0
4*( (1/4)xx - (2/4)x - 6 = 0 )
xx - 2x - 24 = 0
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the above quadratic equation is in standard form, with a=1, b=-2 and c=-24
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to solve the quadratic equation, by using the quadratic formula, copy and paste this:
1 -2 -24
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the quadratic has two real roots at:
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x = 6
x = -4
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the negative root doesn't fit the problem statement, so use the positive root:
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x = 6
y = x + 6
y = 6 + 6
y = 12
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answer:
x = time for engine A alone = 6 hours
y = time for engine B alone = 12 hours
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