SOLUTION: 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 wa

Algebra ->  Rate-of-work-word-problems -> SOLUTION: 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 wa      Log On


   

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 alon e 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 :)
Found 2 solutions by Alan3354, Edwin McCravy:
Answer by Alan3354(69443) About Me  (Show Source):
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
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 :)
The question is:

>>How long will it take each pipe alone to fill the tank?<<
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%2Fx_hours or 1%2Fxtanks%2Fhour

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%2Fy_hours or 1%2Fytanks%2Fhour

>>The empty tank is filled in 10 hours if the two pipes are used together.<<
That means that their combined rate is 1 tank per 10 hours, which is
a rate of 1_tank%2F10_hours or 1%2F10tanks%2Fhour.

So the first equation comes from:

%28matrix%285%2C1%2C%0D%0APipe%2C+%22A%27s%22%2C+%22tank-%22%2C+filling%2C+rate%29%29%22%22%2B%22%22%28matrix%285%2C1%2C%0D%0APipe%2C+%22B%27s%22%2C+%22tank-%22%2C+filling%2C+rate%29%29%22%22=%22%22%28matrix%285%2C1%2C%0D%0ATheir%2C+combines%2C+%22tank-%22%2C+filling%2C+rate%29%29

or     1%2Fx%22%22%2B%22%221%2Fy%22%22=%22%221%2F10

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:

%22%22%2B%22%22%22%22=%22%22%28matrix%283%2C1%2C+One%2C+complete%2C+tank%29%29

      6%2Fx%22%22%2B%22%2218%2Fy%22%22=%22%221

So you have this system of equations:

system%281%2Fx%2B1%2Fy=1%2F10%2C+6%2Fx%2B18%2Fy=1%29

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