Question 850960
Hello :) thank you so much for helping me last time :) i've recommended you to my friends :) can please help me again ? Here's the problem Two pipes, A and B, are used to fill a water tank. The empty tank is filled in 10 hours if the two pipes are used together. If pipe A alone is used for 6 hours and then turned off, pipe B will take over and finish filling the tank in 18 hours. How long will it take each pipe alone to fill the tank?
Thank you :)
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The question is:
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>>How long will it take each pipe alone to fill the tank?<<
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Let x = the number of hours it takes A to fill 1 tank.

That means that A's tank-filling rate is 1 tank per x hours, 
which is the rate of {{{1_tank/x_hours}}} or {{{1/x}}}{{{tanks/hour}}}

Let y = the number of hours it takes B to fill 1 tank.

That means that B's rate is 1 tank per y hours, which is
a rate of {{{1_tank/y_hours}}} or {{{1/y}}}{{{tanks/hour}}}
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>>The empty tank is filled in 10 hours if the two pipes are used together.<<
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That means that their combined rate is 1 tank per 10 hours, which is
a rate of {{{1_tank/10_hours}}} or {{{1/10}}}{{{tanks/hour}}}.

So the first equation comes from:

{{{(matrix(5,1,
Pipe, "A's", "tank-", filling, rate))}}}{{{""+""}}}{{{(matrix(5,1,
Pipe, "B's", "tank-", filling, rate))}}}{{{""=""}}}{{{(matrix(5,1,
Their, combines, "tank-", filling, rate))}}}

or     {{{1/x}}}{{{""+""}}}{{{1/y}}}{{{""=""}}}{{{1/10}}}

pipe A alone is used for 6 hours and then turned off, pipe B will take
over and finish filling the tank in 18 hours.

        part of tank filled   rate    time
pipa A                         1/x     6 
pipe B                         1/y    18
------------------------------------------
Total           1  

To find the part of the tank each filled multiply the rate by the time

        part of tank filled   rate    time
pipa A         6/x             1/x     6 
pipe B        18/y             1/y    18
------------------------------------------
Total           1

So the second equation comes from:

{{{(matrix(11,1,
Part, of, tank, which, A, filled, in, the, first,6,hours))}}}{{{""+""}}}{{{(matrix(11,1,
Part, of, tank, which, B, filled, in, the, next,18,hours))}}}{{{""=""}}}{{{(matrix(3,1, One, complete, tank))}}}

      {{{6/x}}}{{{""+""}}}{{{18/y}}}{{{""=""}}}{{{1}}}

So you have this system of equations:

{{{system(1/x+1/y=1/10, 6/x+18/y=1)}}}

Can you solve that?  If not, email me or tell me in the thank-you note 
and I'll help you solve it.  But please try it on your own, and try to set up
some other problems like this one. 

Edwin</pre>