Question

Pipe a and b running together can fill a cistern in 6 minutes. if b takes 5 minutes more than a to fill the cistern, then the time in which a and b will fill the cistern separately will be respectively?

Answer 1

hey mate hope it helps

Answer 2

The time taken by 'a' to fill the cistern separately is 10 minutes.

The time taken by 'b' to fill the cistern separately is 15 minutes.

Step-by-step explanation:

Let the time taken by a to fill the cistern separately is x.

Given:

• Pipe a and b running together can fill a cistern in 6 minutes.
• Pipe b takes 5 minutes more than a to fill the cistern.

The time taken to fill the cistern by pipe b is (x+5) minutes.

$\rightarrow \: \frac{1}{6} = \frac{1}{a} + \frac{1}{b} \\ \rightarrow \: \frac{1}{6} = \frac{1}{x} + \frac{1}{x + 5} \\ \rightarrow \: \frac{1}{6} = \frac{2x + 5}{x(x + 5)} \\ \rightarrow \: {x}^{2} + 5x = 12x + 30 \\ \rightarrow \: {x}^{2} - 7x - 30 = 0 \\ \rightarrow \: {x}^{2} - 10x + 3x - 30 = 0 \\ \rightarrow \: x(x - 10) + 3(x - 10) = 0 \\ \rightarrow \: (x - 10)(x + 3) = 0 \\ \rightarrow \: x = 10 \: or \: x = - 3$

But time can never be negative so x=10 is valid.

The time taken by a to fill the cistern separately is 'x' i.e. 10 minutes.

The time taken by b to fill the cistern separately is 'x+5' i.e. 15 minutes.