Question

Two pipes running together can fill a tank in 40/13 minutes. If one pipe takes 3 minutes more than the other to fill the tank separately, find the time in which each pipe would fill the tank separately.

Answer 1

Answer:

Time taken by one pipe is 5 minutes and other pipe is 5 + 3 = 8 minutes.

Step-by-step explanation:

Let the time taken to fill the tank by other pipe be x minutes

Portion of tank filled by other pipe in 1 minute = 1/x

Time taken to the tank by one pipe = ( x + 3 ) minutes

Portion of tank filled by one pipe in 1 minute = 1 / ( x + 3 )

Time taken by two pipes to fill the tank = 40/13 minutes

Portion of tank filled by two pipes in 1 minute = 13/40

$\Rightarrow \dfrac{1}{x} + \dfrac{1}{x + 3} = \dfrac{13}{40 }$

$\Rightarrow \dfrac{x + 3 + x}{x(x + 3)} = \dfrac{13}{40 }$

$\Rightarrow \dfrac{2x + 3 }{ {x}^{2} + 3x} = \dfrac{13}{40 }$

⇒ 40( 2x + 3 ) = 13( x² + 3x )

⇒ 80x + 120 = 13x² + 39x

⇒ 13x² + 39x - 80x - 120 = 0

⇒ 13x² - 41x - 120 = 0

⇒ 13x² - 65x + 24x - 120 = 0

⇒ 13x( x - 5 ) + 24( x - 5 ) = 0

⇒ ( 13x + 24 )( x - 5 ) = 0

⇒ 13x + 24 = 0 OR x - 5 = 0

⇒ x = - 24/13 OR x = 5

x can't be negative

⇒ x = 5

Therefore time taken by one pipe is 5 minutes and other pipe is 5 + 3 = 8 minutes.