Two pipe running together can fill …
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Preeti Dabral 4 years, 4 months ago
Let the faster pipe takes x minutes to fill the cistern and the slower pipe will take (x + 3) minutes.
According to question,
{tex}\frac { 1 } { x } + \frac { 1 } { x + 3 } = \frac { 1 } { \frac { 40 } { 13 } }{/tex}
{tex}\Rightarrow \frac { 1 } { x } + \frac { 1 } { x + 3 } = \frac { 13 } { 40 }{/tex}
{tex}\Rightarrow \frac { x + 3 + x } { x ^ { 2 } + 3 x } = \frac { 13 } { 40 }{/tex}
{tex}\Rightarrow{/tex} 13x2 - 41x - 120 = 0
{tex}\Rightarrow{/tex} 13x2 - 65x + 24x - 120 = 0
{tex}\Rightarrow{/tex} 13x(x - 5) + 24(x - 5) = 0
{tex}\Rightarrow{/tex} x = 5 or {tex}x = \frac { - 24 } { 13 }{/tex} (Neglected)
Faster pipe will take 5 minutes and slower pipe will take 8 minutes to fill the cistern
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