# The pool is filled using two tubes in 2h. The first tube fills the pool 3h faster than the second tube. How many hours will it take to fill the tube using only the second tube?

Mar 12, 2016

We must solve by a rational equation.

#### Explanation:

We must find what fraction of the total tub can be filled in 1 hour.

Assuming the first tube is x, the second tube must be x + 3.

$\frac{1}{x} + \frac{1}{x + 3} = \frac{1}{2}$

Solve for x by putting on an equal denominator.

The LCD is (x + 3)(x)(2).

$1 \left(x + 3\right) \left(2\right) + 1 \left(2 x\right) = \left(x\right) \left(x + 3\right)$

$2 x + 6 + 2 x = {x}^{2} + 3 x$

$0 = {x}^{2} - x - 6$

$0 = \left(x - 3\right) \left(x + 2\right)$

$x = 3 \mathmr{and} - 2$

Since a negative value of x is impossible, the solution is x = 3. Therefore, it takes 3 + 3 = 6 hours to fill the pool using the second tube.

Hopefully this helps!