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  • Two pipes running together can fill in   minutes. If one  pipe takes 5 minutes more than the other to fill the tank separatel

Two pipes running together can fill in  11 \frac{1}{9} minutes. If one  pipe takes 5 minutes more than the other to fill the tank separately, find the time in which each pipe would fill the tank separately 

 

 

 

 

 
 
 
 
 

Answers (1)

Let one pipe in A and other in B 

time taken by (A+B) = 11 \frac{1}{9} = 100/9

let time taken by A = x minutes 

Time taken by B = (x+5) minutes 

tank filled by A in 1 minutes + tank filled by B in one minute = tank filled by bottle by both (A and B) 

\frac{1}{x}+ \frac{1}{ (x+5)} = 9/100 \\\\ \frac{( x+5)+x}{x ((x+5))} = 9/100\\\\ ( 2x+5)\times 100 = 9 \times ( x+5) \\\\ 200x + 500 = 9x^2 + 45 x \\\\ 9 x^2 + 45 x -200x -500 = 0 \\\\ 9x^2 - 155x - 500 = 0 \\ 9x^2 - ( 180 -25)x - 500 = 0 \\\\ 9x^2 (x-20)+ 2 5 (x-20 ) = 0 \\ (x-20) \: \:or \: \: x = \frac{-25}{9}

since x \neq negative hence x = 20 minutes 

time taken by A = 20 min 

time taken by B = 25 min 

Posted by

Ravindra Pindel

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