Respuesta :
Answer:
It takes 10 hours using both hoses to fill the pool
Step-by-step explanation:
The rate of the first hose = 1/(x+16)
The rate of the second faster hose is given =1/16.25 = 1/(65/4)=4/65
The combined work rate is 1/x
the sum of the individul work rates equls the combined work rate
1/(x+16) +(4/65) = (1/x)
Multiply each term by the LCM which is (x+16)(65)(x)
The result is: 65x+4x^2+64x=65x+1040
Simplify by subracting 65x from both sides of the equation.
4x^2+64x=1040
Next divide every term by 4
x^2 +16x = 260
subtract 260 from both sides
x^2+16x-260=0
The factors of 260 are: (1 x 260), (2 x 130), (4 x 65), (5 x 52), (10 x 26), (16x 30)
the two that have a difference of 16 are (10 x 26)
the equation factors to
(x +26) (x - 16) = 0
so x = -26 or x = 10
Since you can not have negative time x can not equal -26 it is an extraneous root.
So, the only solution is x =10
It took 10 hours to fill the pool with both hoses running.
