Question

$\huge\mathcal\colorbox{teal}{question}$
A Cristern can be filled by one tap in 4 hours and by another in 5 hours. How long will it take to fill if both tapes are opened together?
$\huge\mathfrak\red{no \: spam}$
​

Answer 1

According to the question, a cistern takes 4 hours to be filled by first tap to its fullest capacity. Therefore, the correct time taken to fill it with water is 4 hours.

Answer 2

$\huge \colorbox{teal}{ Solution}$

Let us call the flow rates of the two taps $a$ and $b$ litres per hour. Then we are given that:

$\huge</p><p>\begin{array}{ll}</p><p>a&=\text{flow rate of 1st tap}= \frac{\text{Cistern capacity}}{4 \:\text{hours}} \\</p><p>b &=\text{flow rate of 2nd tap}=\frac{\text{Cistern capacity}}{5 \:\text{hours}}</p><p>\end{array}</p><p>$

When the taps are running together, the total flow rate into the cistern is $a+b$ litres per hour. Therefore, the time taken to fill the cistern when both taps are open is given by:

$\huge</p><p>\frac{\text{Cistern capacity}}{a+b} \: \text{hours}</p><p>$

Substituting for a and b:

$\huge </p><p>\frac{\text{Cistern capacity}}{\Big(\frac{\text{Cistern capacity}}{4}\Big)+ \Big(\frac{\text{Cistern capacity}}{5}\Big)} = \boxed{\frac{20}{9} \:\text{hours}}</p><p>$

So the answer is $\huge\boxed{\frac{20}{9} \:\text{hours}}$

-----------------------------------------------------------------

• I hope this helps Sweet ❤️! Let me know if you have any other questions. •

-----------------------------------------------------------------