Question

One pipe can fill cistern in (x+2) hours and other pipe can fill the same cistern

in (x+7) hours. If both the pipes when opened together can fill the tank in 6

hours to fill the empty cistern. find the value of x.​

Answer 1

here is the answer hope it helped u

Answer 2

The value of  x= 8.

Explanation:

Given : Time taken by first pipe to fill the cistern = x+2 hours

Time taken by second pipe to fill the cistern =  x+7 hours

If both the pipes when opened together can fill the tank in 6  hours to fill the empty cistern , then we have the following equations:

$\dfrac{1}{x+2}+\dfrac{1}{x+7}=\dfrac{1}{6}\\\\ \dfrac{x+7+x+2}{(x+2)(x+7)}=\dfrac{1}{6}\\\\\dfrac{2x+9}{x^2+9x+14}=\dfrac{1}{6}\\\\ 6(2x+9)=x^2+9x+14\\\\ 12x+54=x^2+9x+14\\\\ x^2-3x-40=0\\\\ x^2-8x+5x-40=0\\\\ (x-8)(x+5)=0\\\\ x=8 , -5$

If x = -5 , then x+2 = -5+2=-3 , which is not possible as time cannot b negative.

So , the value of  x= 8.

# Learn more :

Pipe A can fill a cistern in 10 hours and pipe B can empty the filled cistern in 15 hours. if both the pipes are opened together in cistern then in how much time cistern will be filled

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