Question

it can take 12 hours to fill swimming pool using two pipes if the pipes of larger diameter is used for 4 hours only half of the pool can be filled how long would it take for each pipe of fill the pool separately​

Answer 1

Appropriate Question :-

• It can take 12 hours to fill a swimming pool using two pipes. If the pipe of larger diameter is used for four hours and the pipe of smaller diameter for 9 hours, only half of the pool can be filled. How long would it take for each pipe to fill the pool separately?

Answer :-

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 = 1/x
• In 1 hour pipe B can fill the pool= 1/y

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

If the are together then in 1 hour they fill the pool.

⇒ 1/x + 1/y = 1/12 −−−−(1)

Now

• In 4 hour pipe A can fill the pool is= 4/x
• In 9 hour pipe B can fill the pool is= 9/y

than they fill half of the pool,so

⇒ 4/x + 9/y = 1/2 −−−−−(2)

Now Let

1/x = P & 1/y = Q and putting in equation 1 &2, than P + Q = 1/12

⇒12P + 12Q = 1 −−−−(3)

And

⇒4P + 9Q = 1/2

⇒8P+18Q = 1 −−−−−(4)

Now solving equation 3 & 4

Equation (3) multiplying by 2 and (4) multiplying by 3 and substract.

⇒−30Q = −1

⇒Q = 1/30

now put value of Q in equation 3

We get P = 1/20

So we found,

P = 1/20 & Q = 1/30

So x = 20 and y = 30

• Hence the A pipe would take 20 hours and the pipe B would take 30 hours separately

Answer 2

Answer :-

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 = 1/x

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

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

If the are together then in 1 hour they fill the pool.

⇒ 1/x + 1/y = 1/12 −−−−(1)

Now

In 4 hour pipe A can fill the pool is= 4/x

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

than they fill half of the pool,so

⇒ 4/x + 9/y = 1/2 −−−−−(2)

Now Let

1/x = P & 1/y = Q and putting in equation 1 &2, than P + Q = 1/12

⇒12P + 12Q = 1 −−−−(3)

And

⇒4P + 9Q = 1/2

⇒8P+18Q = 1 −−−−−(4)

Now solving equation 3 & 4

Equation (3) multiplying by 2 and (4) multiplying by 3 and substract.

⇒−30Q = −1

⇒Q = 1/30

now put value of Q in equation 3

We get P = 1/20

So we found,

P = 1/20 & Q = 1/30

So x = 20 and y = 30

Hence the A pipe would take 20 hours and the pipe B would take 30 hours separately