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?
first pipe fills in f hours so 1 pool/f hours rate
second pipe fill in s hours so 1 pool /s hours rate
rate with both working = (1/f+1/s)pools/hour
so (1/f + 1/s) T = 1
f = 9 + T
f = s - 7 so s = f+7 = 9+T +7 = 16 + T
1/(T+9) + 1/(T+16) ] = 1/T
(T+16)+ (T+9) =(T^2+ 25 T + 144)/T
2 T^2 + 25 T = T^2 + 25 T +144
T^2 = 144
T = 12
Let T1 be the time for pipe1 to fill the pool, T2...
so the combined time for both pipes is
1/T12 = 1/T1 + 1/T2 or T12=T1*T2/(T1+T2)
given T1=9+T12
and T1=T2-7
t1=9 + T1*T2/(T1+T2) replacing T1 with T2-7
T2-7=9 + (T2-7)(T2)/(2T2-7) lets replace t2 with x
(x-7)(2x-7)=9(2x-7)+x^2-7x
you can do all that, it looks to be a quadratic.
once x (T2) is found, then
x-7 is t1
so the combined time is (T1*T2/(T1+T2))
To find the time it takes to fill the pool when both pipes are working together, we need to set up an equation using the given information. Let's assume that it takes the first pipe x hours to fill the pool.
According to the problem, it takes the first pipe 9 more hours to fill the pool than the first and second pipes together. This means that the first and second pipes together can fill the pool in x + 9 hours.
It also mentions that it takes the first pipe 7 less hours than the second pipe would take alone. So, if we assume it takes the second pipe y hours to fill the pool, then the first pipe would take y - 7 hours to fill the pool.
Now, let's set up the equation:
1st pipe + 2nd pipe = 1st pipe alone
x + (x + 9) = y - 7
Simplifying the equation, we get:
2x + 9 = y - 7
Since we want to find the time it takes when both pipes are working together, let's solve for y (time for the second pipe):
y = 2x + 16
Now, we know that the time it takes for the first and second pipes together is x + 9. So, we can set up another equation:
1st pipe + 2nd pipe = x + 9
Substituting the value of y from the previous equation, we get:
x + (2x + 16) = x + 9
Simplifying the equation:
3x + 16 = x + 9
2x = -7
x = -7/2
Since time cannot be negative, we ignore the negative solution. Therefore, the time it takes for the first pipe to fill the pool is x = -7/2.
It seems there is an error in the information provided or the problem is unsolvable. Please double-check the problem statement or provide additional information.
If the two together take z hours, then
1/x + 1/y = 1/z
x = z+9
x = y-7
now just crank it out