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  • Two water taps together can fill a tank in  hours. The tap with longer diameter takes 2 hours less than the tap with smaller one to fill the

Two water taps together can fill a tank in 1\frac{7}{8} hours. The tap with longer diameter takes 2 hours less than the tap with smaller one to fill the tank separately. Find the time in which each tap can fill the tank separately.

 

 
 
 
 
 

Answers (1)

Lets assume,

smaller diameter pipe alone takes x hours to fill the tank.

then larger diameter pipe alone takes (x-2) hours,

So the 1 hour work of larger pipe = \frac{1}{x-2}

1 hour work of smaller pipe = \frac{1}{x}

Both takes 15/8 hour to fill,

So quantity filled = 8/15

According to the question,

\frac{1}{x}+\frac{1}{x-2}=\frac{8}{15}

\frac{x-2+x}{x(x-2)}=\frac{8}{15}

\frac{2x-2}{(x^2-2x)}=\frac{8}{15}

30x-30=8x^2-16x

8x^2-46x+30=0

8x^2-40x-6x+30=0

8x(x-5)-6(x-5)=0

\left (8x-6 \right )(x-5)=0

Values of x = 5 and 3/4

If x=3/4 then the time taken by larger diameter pipe will be negative so the value of x = 5.

Time taken by smaller pipe = 5 hours.

Time taken by larger pipe = 3 hours.

Posted by

Safeer PP

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