It takes the first pipe 9 more hours to fill the pool than the first and the second pipes together and 7 less hours than it would take the second pipe if it was working alone. How long would it take to fill up the pool if both pipes were working together?
1st and 2nd pipe: X hours.
1st pipe: x+9 hours.
2nd pipe: (x+9) +7 = x+16.
1/(x+9) +1/(x+16) = 1/x
(x+16)/(x+9)(x+16) + (x+9)/(x+9)(x+16) = 1/x
(2x+25)/(x+9)(x+16) = 1/x
(x+9)(x+16) = 2x^2+25x
x^2+16x+9x+144 = 2x^2+25x
x^2 = 144
X = 12 hours.
Let's break down the information given in the problem:
Let's assume the time it takes for the first pipe to fill the pool on its own is "x" hours.
The time it takes for the second pipe to fill the pool on its own would be "x - 7" hours. (7 hours less than the first pipe alone)
According to the problem, it takes the first pipe 9 more hours to fill the pool than the time it takes for both pipes together. So, if we add 9 hours to the time it takes for both pipes together, it should be equal to the time it takes for the first pipe alone.
Therefore, the equation we can form is: x = (x + x - 7) + 9
Simplifying this equation:
x = 2x - 7 + 9
x = 2x + 2
Bringing the 2x term to the left side, we get:
x - 2x = 2
-x = 2
Multiplying both sides by -1, we have:
x = -2
This is an invalid solution since time cannot be negative. It means there is no valid time for the first pipe to fill the pool on its own.
Hence, there might be an error in the given problem. Please double-check the details and provide the correct information.