Question

two drain pipes, working together, can drain a tank in 4 hours. Working alone, it would take the smaller pipe 6 hours longer than it would take the larger pipe to drain the tank. How long would it take the smaller pipe alone to drain the tank.

Answer 1

Answer:

12 hours

Step-by-step explanation:

Let the larger pipe can drain the tank in x hours

Than, time taken by smaller tank to drain the tank= (x+6) hours

If working togather, both pipe can drain the tank= 4 hours

A.T.Q

$\frac{1}{x}$  + $\frac{1}{x+6}$=  $\frac{1}{4}$

$\frac{x+x+6}{x(x+6)}$=  $\frac{1}{4}$

$\frac{2x+6}{x^{2}+6x }$=  $\frac{1}{4}$

8 x +24= $x^{2}$ + 6 x

$x^{2}$ - 2 x- 24= 0

$x^{2}$ -6 x+ 4 x -24=0

x(x-6) + 4(x-6)= 0

(x-6)(x+4)=0

X= 6, X=-4 is rejected

Hence, time taken by larger tank to fill the drain= 6 hours

Hence, time taken by smaller tank to drain the tank = 6+6= 12 hours

Hence, the correct answer is 12 hours