SOLUTION: I have a tank that can be filled by a small pipe in 12 hours or by a large pipe in 8 hours. Suppose I start filling the tank with the large pipe for two hours. After that 2 hours i

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Question 548244: I have a tank that can be filled by a small pipe in 12 hours or by a large pipe in 8 hours. Suppose I start filling the tank with the large pipe for two hours. After that 2 hours is up, I use both pipes and continue filling the tank for a length of time, t. I then turn off the large pipe and it takes 2 more hours to fill the tank with just the small pipe. How long of a time is t?
Found 2 solutions by ankor@dixie-net.com, josmiceli:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
I have a tank that can be filled by a small pipe in 12 hours or by a large pipe in 8 hours.
Suppose I start filling the tank with the large pipe for two hours.
After that 2 hours is up, I use both pipes and continue filling the tank for a length of time, t.
I then turn off the large pipe and it takes 2 more hours to fill the tank with just the small pipe.
How long of a time is t?
:
Let the completed task = 1 (a full tank)
:
from the given information:
(t+2) = filling time of the large pipe
and
(t+2) = filling time of the smaller
:
%28t%2B2%29%2F12 + %28t%2B2%29%2F8 = 1
Multiply by 24, results:
2(t+2) + 3(t+2) = 24
2t + 4 + 3d + 6 = 24
2t + 3t = 24 - 10
5t = 14
t = 14%2F5
t = 2.8 hrs
;
:
See if that checks out
%282.8%2B2%29%2F12 + %282.8%2B2%29%2F8 =
4.8%2F12 + 4.8%2F8 =
.4 + .6 = 1

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
In words:
( portion of the tank filled ) = ( rate of filling ) x ( time spent filling )
Rate using small pipe: ( 1 tank ) / ( 12 hrs )
Rate using large pipe: ( 1 tank ) / (8 hrs )
----------------------------------
Using large pipe for 2 hrs:
Portion of tank filled is +%281%2F8%29%2A2+=+1%2F4+
There is +3%2F4+ of the tank left to be filled
----------------------------------
Using both pipes, add their rates of filling
to get rate together
+1%2F12+%2B+1%2F8+=+R+
+2%2F24+%2B+3%2F24+=+R+
+24R+=+2+%2B+3+
+R+=+5%2F24+
Now the fraction of the tank left to be filled
is +3%2F4+-+%285%2F24%29%2At+
------------------
Using the small pipe for 2 more hrs
+18%2F24+-+%285%2F24%29%2At+=+%281%2F12%29%2A2+
+18%2F24+-+%285%2F24%29%2At+=+%282%2F24%29%2A2+
+18%2F24+-+%285%2F24%29%2At+=+4%2F24+
+18+-+5t+=+4+
+5t+=+18+-+4+
+5t+=+14+
+t+=+14%2F5+ hrs
+%284%2F5%29%2A60+=+48+ min
t is 2 hrs and 48 min
I may have made a mistake, but
I think the method is good