Question

Pump $A$ can fill a tank of water in $5$ hours.

Pump $B$ fills the same tank in $8$ hours.

How long does it take the two pumps working together to fill the tank?

Answer 1

Step-1: Calculating the rate of flow:

Let the Volume of the tank be $x$.

Given,

The pump $A$ can fill a tank of water in $5$ hours

The pump $B$ fills the same tank in $8$ hours

For one hour pump $A$fill one-fifth of the volume of the tank

Flow rate =$\frac{\text{volume}}{\text{time}}$$\Rightarrow \frac{x}{5}$

For one hour pump $B$ fill one-eighth of the volume of the tank

$\Rightarrow \frac{x}{8}$

The flow rate of two pumps working together is

$$\begin{gathered} \Rightarrow \frac{x}{5}+\frac{x}{8}=\frac{8x+5x}{40}\left[\text{taking l.c.m in denominator}\right] \\ =\frac{13x}{40}\to \left(i\right) \end{gathered}$$

Step-2: Finding the number of hours to fill the tank when two pumps working together

We know that,

Flow rate =$\frac{\text{volume}}{\text{time}}\Rightarrow Q=\frac{V}{t}$

Equating the equation $\left(i\right)$ with this

$$\begin{gathered} \Rightarrow \frac{V}{t}=\frac{13x}{40} \\ \Rightarrow \frac{x}{t}=\frac{13x}{40}\left[\because V=x\right] \\ \Rightarrow t=\frac{40x}{13x} \\ \Rightarrow t=3.08 \end{gathered}$$

Therefore, it takes $3.08$ hours to fill the tank when two pumps work together.