untitled

or, ̧ ̧
¹

·

̈ ̈

©

§



1 2

1 1

2 t t

x

u

Subtracting equation (ii) from equation (i) we get,

̧ ̧

¹

·

̈ ̈

©

§



2 1

2 1 1

t t

v x

or, ̧ ̧
¹

·

̈ ̈

©

§



2 1

1 1

2 t t

x

v

Hence, speed of current is ̧ ̧
¹

·

̈ ̈©

§



2 1

1 1

2 t t

x km per hour

and speed of boat is ̧ ̧
¹

·

̈ ̈

©

§



1 2

1 1

2 t t

x km per hour.

Example 4. A pipe can fill up an empty tank in 12 minutes. Another pipe flows out
14 litre of water per minute. If the two pipes are opened together and the empty tank
is filled up in 96 minutes, how much water does the tank contain?

Solution : Let x litre of water flows in per minute by the first pipe and the tank can
containy litre of water.
According to the question, the tank is filled up by first pipe in 12 minutes,

? y 12 x.......(i)

Again, the empty tank is filled up by the two pipes together in 96 minutes.

?y 96 x 96 u 14 .........(ii)

From equation (i), we get,
12

y

x

putting the value of x in equation (ii), we get,

96 14

12

y 96 uy u

or,y 8 y 96 u 14

or, 7 y 96 u 14

or, 192
7

96 14

u

y

Hence, total 192 litre of water is contained in the tank.