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

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): You can put this solution on YOUR website!
.

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.

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For a wide variety of similar solved joint-work problems with detailed explanations see the lessons
    - Using Fractions to solve word problems on joint work
    - Solving more complicated word problems on joint work
    - Selected joint-work word problems from the archive
in this site.

Read them and get be trained in solving joint-work problems.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic "Rate of work and joint work problems" of the section "Word problems".

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