Question

it takes 12 hours to fill a swimming pool using two pipes . if the pipe of larger diameter is used for 9 hours, only half of the pool is filled . how long would each pipe take to fill the swimming pool​

Answer 1

Answer:

It is given that if both pipes are together then they take 12 hours to fill the pool. Now, in 4 hour pipe A can fill the pool is = 1x×4=4x. So, in 9 hour pipe B can fill the pool is = 1y×9=9y.

Answer 2

Let there are two pipes A and B and diameter of A is larger than B.
Now suppose that
Pipe A take x hours and Pipe B takes y hours to fill the pool separately .
In 1 hour pipe A can fill the pool =
x
1
​


In 1 hour pipe B can fill the pool=
y
1
​

If both pipe are together then they take 12 hour to fill the pool.

If the are togther then in 1 hour they fill the pool.
x
1
​
+
y
1
​
=
12
1
​
−−−−(1)
Now
In 4 hour pipe A can fill the pool is=
x
4
​


In 9 hour pipe B can fill the pool is=
y
9
​

than they fill half of the pool,so
x
4
​
+
y
9
​
=
2
1
​
−−−−−(2)
Now Let
x
1
​
=P &
y
1
​
=Q and puuting in equation 1 &2, than
P+Q=
12
1
​

⇒12P+12Q=1−−−−(3)
And
4P+9Q =
2
1
​

⇒8P+18Q=1−−−−−(4)
Now solving equation 3 & 4
Equation (3) multiplying by 2 and (4) multiplying by 3 and substract.
⇒−30Q=−1
⇒Q=
30
1
​

now put value of Q in equation 3
We get P=
20
1
​

So we found

P=
20
1
​
& Q=
30
1
​

So x=20 and y=30
Hence the A pipe would take 20 hours and the pipe B would take 30 hours separately .

Please mark my answer as the brainliest .