Welcome to Westonci.ca, the Q&A platform where your questions are met with detailed answers from experienced experts. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
Sagot :
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.
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.
