SOLUTION: One pipe can empty a tank 3 times faster than another pipe. Starting with a full tank, both pipes take 6 hrs to empty the tank. How long does it take the faster pipe working alone

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Question 927307: One pipe can empty a tank 3 times faster than another pipe. Starting with a full tank, both pipes take 6 hrs to empty the tank. How long does it take the faster pipe working alone to empty a full tank?
Found 3 solutions by stanbon, josmiceli, TimothyLamb:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
One pipe can empty a tank 3 times faster than another pipe.
slower pipe:: time = 3x hrs ; rate = 1/(3x) job/hr
faster pipe:: time = x hrs ; rate = 1/x job/hr
---------------------
Starting with a full tank,if both pipes are turned on,it takes 6 hrs.to empty the ta/hrnk.
Together:: time = 6 hrs/job ; rate = 1/6 job
--------------------------------------------------
how long does it take the faster pipe working alone to empty a full tank?
Equation::
rate + rate = together rate
1/x + 1/(3x) = 1/6
6 + 2 = x
-----
x = 8 hrs (time for the faster pipe to do the job)
3x = 24 hrs (time for the slower pipe to do the job)
===============
Cheers,
Stan H.
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Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +R+ = the rate of emptying of
the slowest pipe in tankfuls / hrs
+3R+ = the rate of emptying of
the other pipe in tankfuls / hrs
-------------------------------
Add the rates of emptying to get
their rate emptying together
--------------------------
+1%2F6+ = rate of emptying together
in tankfuls / hrs
+R+%2B+3R+=+1%2F6+
+4R+=+1%2F6+
+R+=+1%2F24+
+3R+=+1%2F8+
The faster tank takes 8 hrs to empty
the tank alone
---------------
check:
+1%2F24+%2B+1%2F8+=+1%2F6+
+1%2F24+%2B+3%2F24+=+4%2F24+
OK
------------------------
Note that if there were both emptying and
filling pipes, then the emptying rates
would have minus signs and the filling
rates would have plus signs




Answer by TimothyLamb(4379) About Me  (Show Source):
You can put this solution on YOUR website!
r = w/t
---
x = rate of slow pipe
y = rate of fast pipe
y = 3x
---
1/(x + y) = 6
1 = 6(x + y)
1 = 6x + 6y
1 = 6x + 6*3x
1 = 6x + 18x
1 = 24x
x = 1/24
---
y = 3x
y = 3/24
y = 1/8
---
r = w/t
t = w/r
t = w/y
t = 1/(1/8)
t = 8
---
answer:
How long it takes the faster pipe working alone to empty a full tank = 8 hours
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