Question

B. To fill a swimming pool two pipes are to be used. If
the pipe of larger diameter is used for 4 hours and
the pipe of smaller diameter for 9 hours, only half
the pool can be filled. Find, how long it would take
for each pipe to fill the pool separately, if the pipe
of smaller diameter takes 10 hours more than the
nine of larger diameter of:11 hel
14​

Answer 1

Step-by-step explanation:

Suppose that x hours to the total time taken by the larger pipe and y hour of the smaller pipe

Now,

x

4

+

y

9

=

2

1

...........(1)

smaller diameter takes 10 hour more than the larger dia. pipe.

y=x+10.............(ii)

Put the value eq (i) from eq (ii)

x

4

+

x+10

9

=

2

1

⇒

x(x+10)

4(x+10)+9x

=

2

1

⇒26x+80=x

2

+10x

⇒x

2

−16x−80=0..........(iii)

Solve eq (iii)

(x−20)(x+4)=0

x=20,x=−4

The value of x can not be -ve so that the value of x=20.

So that the larger dia pipe fill the tank x=20 hour and smaller diameter pipe fill the tank y=x+10=20+10=30 hour

x=20hour

y=30hour

Answer 2

Answer:

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Step-by-step explanation:

Suppose that x hours to the total time taken by the larger pipe and y hour of the smaller pipe

Now, x4+y9=21...........(1)

smaller diameter takes 10 hour more than the larger dia. pipe.

y=x+10.............(ii)

Put the value eq (i) from eq (ii)

x4+x+109=21

⇒x(x+10)4(x+10)+9x=21

⇒26x+80=x2+10x

⇒x2−16x−80=0..........(iii)

Solve eq (iii)

(x−20)(x+4)=0

x=20,x=−4

The value of x can not be -ve so that the value of x=20.

So that the larger dia pipe fill the tank x=20 hour and smaller diameter pipe fill the tank y=x+10=20+10=30 hour

x=20hour. y=30hour