SOLUTION: Two pipes together can fill the reservoir in 6 hours and 40 minutes. Find the time each alone will take to fill the reservoir if one of the pipes can fill it in 3 hours less than t

Question 1042119: Two pipes together can fill the reservoir in 6 hours and 40 minutes. Find the time each alone will take to fill the reservoir if one of the pipes can fill it in 3 hours less than the other.
Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Two pipes together can fill the reservoir in 6 hours and 40 minutes. Find the time each alone will take to fill the reservoir if one of the pipes can fill it in 3 hours less than the other.
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Note:: 6 hr 40 min = 6 2/3 hrs = 20/3 hrs/job
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together rate:: 3/20 job/hr
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slower pipe rate:: 1/x job/hr
faster pipe rate:: 1/(x-3) job/hr
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Equation::
rate + rate = together rate
1/x + 1/(x-3) = 3/20
20(x-3) + 20x = 3x(x-3)
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40x - 60 = 3x^2 - 9x
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3x^2 - 49x + 60 = 0
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x = 15 hr (slower time)
x-3 = 12 hr (faster time)
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Cheers,
Stan H.
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Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = time in hrs to fill reservoir by
the slower-filling pipe
= time in hrs to fill reservoir by
the faster-filling pipe
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Rate of filling by slower-filling pipe:
[ 1 reservoir filled ] / [ t hrs ]
Rate of filling by faster-filling pipe:
[ 1 reservoir filled ] / [ t - 3 hrs ]
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Add the rates of filling to get the rate with
both pipes filling together
( first convert minutes to hrs )

Multiply both sides by

Use quadratic formula

( note that the negative square root will not work )

and

The pipes can fill the reservoir in 12 hrs and 15 hrs each
working alone
-----------------------
check:

OK
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