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

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> 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      Log On


   

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) About Me  (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) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = time in hrs to fill reservoir by
the slower-filling pipe
+t+-+3+ = 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 )
+1%2Ft+%2B+1%2F%28+t-3+%29+=+1%2F6.667+
+1%2Ft+%2B+1%2F%28+t-3+%29+=+3%2F20+
Multiply both sides by +t%2A%28+t-3+%29%2A20+
+20%2A%28+t-3+%29+%2B+20t+=+3t%2A%28+t-3+%29+
+20t+-+60+%2B+20t+=+3t%5E2+-+9t+
+3t%5E2+-+49t+%2B+60+=+0+
Use quadratic formula
+t+=+%28+-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+3+
+b+=+-49+
+c+=+60+
+t+=+%28+-%28-49%29+%2B-+sqrt%28+%28-49%29%5E2-4%2A3%2A60+%29%29%2F%282%2A3%29+
+t+=+%28+49+%2B-+sqrt%28+2401+-+720+%29%29%2F6+
+t+=+%28+49+%2B-+sqrt%28+1681+%29%29%2F6+
+t+=+%28+49+%2B+41+%29+%2F+6+
( note that the negative square root will not work )
+t+=+90%2F6+
+t+=+15+
and
+t+-+3+=+12+
The pipes can fill the reservoir in 12 hrs and 15 hrs each
working alone
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check:
+1%2Ft+%2B+1%2F%28+t-3+%29+=+1%2F%28%2820%2F3%29%29+
+1%2F15+%2B+1%2F12+=+3%2F20+
+4%2F60+%2B+5%2F60+=+9%2F60+
+9%2F60+=+9%2F60+
OK