SOLUTION: a pipe can fill a tank in 12 hours and another can empty in 24 hours. if both the pipes are used, with the first pipe running for 2 hours and second pipe running for 1 hour, altern

Algebra ->  Proofs -> SOLUTION: a pipe can fill a tank in 12 hours and another can empty in 24 hours. if both the pipes are used, with the first pipe running for 2 hours and second pipe running for 1 hour, altern      Log On


   

Question 706228: a pipe can fill a tank in 12 hours and another can empty in 24 hours. if both the pipes are used, with the first pipe running for 2 hours and second pipe running for 1 hour, alternatively, starting with the first pipe, then how long will it take to fill the tank
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
In other words, every 3 hours, the 1st pipe fills for 2 hours
and the 2nd pipe empties for 1 hour.
Let +3t+ = time in hours to fill the tank
+2t+ will be the 1st pipe's time filling
+t+ will be the 2nd pipe's time emptying
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( 1 tank ) / ( 12 hrs ), or +1%2F12+ is the 1st pipe's rate
( 1 tank ) / ( 24 hrs ) or +1%2F24+ is the 2nd pipe's rate
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Note that (rate)x(time) = fraction of tank filled or emptied
+%281%2F12%29%2A2t+-+%281%2F24%29%2At+=+1+
This says ( fraction of tank filled ) - ( fraction emptied ) = ( 1 tank filled )
Divide both sides by +t+
+2%2F12+-+1%2F24+=+1%2Ft+
+4%2F24+-+1%2F24+=+1%2Ft+
+3%2F24+=+1%2Ft+
+1%2F8+=+1%2Ft+
+t+=+8+
+3t+=+24+
It will take 24 hrs to fill the tank