SOLUTION: A small pipe can fill a tank in 8 min more time than it takes a larger pipe to fill the same tank. Working together, the pipes can fill the tank in 3 min. How long would it take ea
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Question 1073931: A small pipe can fill a tank in 8 min more time than it takes a larger pipe to fill the same tank. Working together, the pipes can fill the tank in 3 min. How long would it take each pipe, working alone, to fill the tank?
smaller pipe ......... min
larger pipe ......... min Answer by ikleyn(52794) (Show Source):
Let x be the time for the large pipe to fill the tank working alone, in minutes.
Then the time for the small pipe to fill the tank working alone is (t+8) minutes.
The larger pipe fills of the tank volume per minute.
The smaller pipe fills of the tank volume per minute.
The two pipes fill of the tank volume, working simultaneously.
The condition says
= 1.
---> 3*(x+8) + 3x = x*(x+8) ---> = ---> (x-6)*(x+4) = 0 ---->
the only positive root is t= 6 minutes.
Answer. 6 minutes for the large pipe to fill the tank, and 6 + 8 = 14 minutes for the small pipe.
