Question

Two pipes p and q together can fill a cistern in 4 hours. If they had been opened separately, then q would have taken 6 hours more than p to fill the cistern. How much time is to be taken by p to fill cistern separately

Answer 1

Answer:

I don't know this one as soon as I get it I will be giving you the answer

Answer 2

Given:

Time taken by $P$ and $Q$ together to fill the tank $=4hours$

To find:

Time taken by $P$ alone to fill the cistern.

Solution:

We have been given that the time taken by $Q$ would take 6 hours more to fill the cistern than what time $P$ would take.

Let, $P$ take $T$ hours to fill the cistern alone.

Hence, Time taken by $Q$ alone to fill the cistern $=(T+6)hours$  

Now,

$P$ takes $T$ hours to fill 1 cistern full. Hence, the volume that will be filled in 1 hour will be $\frac{1}{T}$.

Similarly, volume of the cistern filled in $(T+6)$ hours will be $\frac{1}{T+6}$.

Now,

We have been given that $P$ and $Q$ will together fill the cistern in 4 hours.

Hence, it can be written as

$\frac{1}{T}+ \frac{1}{T+6}= \frac{1}{4}$

$\frac{2T+6}{T(T+6)} =\frac{1}{4}$

$4(2T+6)=T(T+6)$

$8T+24=T^{2}+6T$

$T^{2}-2T-24=0$

$T^{2} -6T+4T-24=0$

$T(T-6)+4(T-6)=0$

$(T+4)(T-6)=0$

$T=-4,6$

Time cannon be negative. Hence, time taken by $P$ alone to fill the cistern is 6 hours.

Thus, time taken by $Q$ alone to fill the cistern will be $=6+(6)=12$ hours.

Final answer:

Hence, to fill the cistern alone, P will take 6 hours.