In 1 minute portion of tank filled by filling pipe=1/x

In 1 minute portion of tank emptied by 2nd pipe=1/x+5

So net portion of tank filled in. 1 minute if both operate simultaneously =[1/x]-[1/x+5]=5/(x+5)(x)….(1)

According to the given condition in 16.8 minutes the tank gets filled when both pipes are operated simultaneously.

So in 1 minute portion of tank filled =1/16.8….(2)

From(1) and (2) we have

5/(x+5)(x)=1/16.8

X^2+5x-84=0

Solving this we get x=7 minutes.

Hope it helps

Given:
- Time taken to fill the tank by one pipe = 'x' minutes
- Time taken to empty the tank by another pipe = (x+5) minutes
- Time taken to fill the tank when both pipes are opened together = 16.8 minutes

To Find:
The value of 'x'

Solution:

Let's assume that the capacity of the tank is 1 unit (for simplicity).

Step 1:
We need to determine the filling rate and emptying rate of the pipes.

- Filling rate of the first pipe = 1/x (1 tank capacity per minute)
- Emptying rate of the second pipe = 1/(x+5) (1 tank capacity per minute)

Step 2:
When both pipes are opened together, the effective filling rate will be the sum of the filling rate of the first pipe and the emptying rate of the second pipe.

Effective filling rate = 1/x + 1/(x+5) (1 tank capacity per minute)

Step 3:
Using the information given in the question, we can set up the equation:

Effective filling rate * Time taken = Tank capacity

(1/x + 1/(x+5)) * 16.8 = 1

Simplifying the equation:

16.8/x + 16.8/(x+5) = 1

Step 4:
To solve the equation, we can multiply both sides by x(x+5) to eliminate the denominators:

16.8(x+5) + 16.8x = x(x+5)

16.8x + 84 + 16.8x = x^2 + 5x

33.6x + 84 = x^2 + 5x

Rearranging the equation:

x^2 - 28.6x - 84 = 0

Step 5:
We can solve the quadratic equation using factoring or the quadratic formula. However, in this case, the equation does not factor nicely, so we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this equation, a = 1, b = -28.6, and c = -84.

Calculating the values:

x = (-(-28.6) ± √((-28.6)^2 - 4(1)(-84))) / (2(1))

x = (28.6 ± √(817.96 + 336)) / 2

x = (28.6 ± √1153.96) / 2

x = (28.6 ± 33.96) / 2

Step 6:
Since time cannot be negative, we discard the negative value:

x = (28.6 + 33.96) / 2

x = 62.56 / 2

x = 31.28

Therefore, the value of 'x' is 31.28 minutes.