Question

Two pipes can fill a tank in 10 and 14 minutes respectively and a waste pipe can empty 4 gallons per minute. if all the pipes working together can fill the tank in 6 minutes, what is the capacity of the tank?

Answer 1

capacity of tank be x gallons
work donebu pipe a in 1 minute = x/10
tank filled by pipe 2 in 1 min =x/14
work done in1 min by three pipes =x/6
thus
$\frac{x}{10} + \frac{x}{14} - 4 = \frac{x}{6} \\ \frac{21x + 15x - 35x}{210} = 4 \\ \frac{x}{210} = 4 \\ x = 210 \times 4 = 840gallon$

Answer 2

Given:

Two pipes can fill a tank in 10 and 14 minutes respectively. A waste pipe can empty 4 gallons per minute.

To find:

The capacity of the tank.

Solution:

$Pipe A fills the tank =10 \mathrm{~mins} \\Pipe B fills the tank=14 \mathrm{~mins}$

$Pipe C empties the water = 4 gallons/min$

$All pipes together fill the tank =6 \mathrm{~min} \\Work done by the waste pipe in 1 minute =\frac{1}{6}-\left(\frac{1}{10}+\frac{1}{14}\right) \\ \begin{array}{l}=\frac{1}{6}-\frac{6}{35} \\\\=-\frac{1}{210}\end{array} Negative sign means emptying \\ \therefore Volume of \frac{1}{210} part =210 gallons\\ \therefore Total capacity of tank = 210 \times 4= 840 gallons.$

Therefore, the capacity of the tank is 840 gallons.