Question

(1) It takes 12 hours to fill a swimming pool using two pipes of different

diameters. If the pipe of larger diameter is kept open for 4 hours and the pipe

with smaller diameter for 9 hours, only half of the pool can be filled. How

long will it take for each pipe to fill the pool separately ?


(2) Solve for x and y.

ax + by = a - b; bx — ay = a + b.



Please solve and answer both questions
It's my Homework and I have to submit it tomorrow.​

Answer 1

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 =

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

Answer 2

Answer:

let there are two pipes a and b okay