Question 45662
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Hi again,

I need some assistance with this mixture problem:

It takes a pipe 10 minutes less than another one to fill a tank of water. Both pipes together
can fill the tank in 12 minutes. How long will it take each one to fill the tank separately?

I am having trouble on how to start setting the equation up.

Thanks again,
Lou

Let time it takes FASTER pipe, be F
Then time it takes the SLOWER pipe = F + 10
Fraction of tank filled by FASTER pipe in 1 munute: {{{1/F}}}
Fraction of tank filled by SLOWER pipe in 1 munute: {{{1/(F + 10)}}}
With the time taken by both pipes to fill the tank being 12 minutes, we get the following equation: {{{1/F + 1/(F + 10) = 1/12}}}
 12(F + 10) + 12F = F(F + 10) ------ Multiplying by LCD, 12F(F + 10)
    {{{12F + 120 + 12F = F^2 + 10F}}}
         {{{24F + 120 = F^2 + 10F}}}
{{{F^2 + 10F - 24F - 120 = 0}}}
     {{{F^2 - 14F - 120 = 0}}}
  (F - 20)(F + 6) = 0
           F - 20 = 0     OR     F + 6 = 0____F = - 6 (ignore)
Time faster pipe takes to fill tank, by itself, or F = <font color =red><font size = 4><b>20 minutes</font></font></b>
Time slower pipe takes to fill tank, by itself, or F + 10 = 20 + 10 = <font color =red><font size = 4><b>30 minutes</font></font></b>

The answer can also be seen HERE ====> Question 742195: One pipe can fill a tank in 20 minutes, while
another takes 30 minutes to fill the same tank. How long would it take the two pipes together to fill the tank?</pre>