Question

pipe A can fill an empty tank in 5 hours while pipe B can empty the full yank in 6 hours. if both are opened at the same time in the empty tank, how much time will they take to fill it up completely?​

Answer 1

GivEn:

• Pipe A can fill a tank in 5 hours
• Pipe B can empty a tank in 6 hours.

To find:

• If tank is empty and both pipe A and B are opened together then how time they take to fill tank

Solution:

Here,

Given that pipe A can fill tank in 5 hours.

∴ A will fill 1/5 part of tank in 1 hour. ••••••(1)

Given that pipe B can empty tank in 6 hours

∴ B will fill -1/6 part of tank in 1 hour ••••••(2)

Now, add equation 1 and 2 to get part of tank they will fill in 1 hour :

=> $\large{\tt{\dfrac{1}{5} +(-\dfrac{1}{6})}}$

=> $\large{\tt{\dfrac{1}{5}-\dfrac{1}{6}}}$

=> $\large{\tt{\dfrac{6-5}{30}}}$

=> $\large{\tt{\dfrac{1}{30}}}$

∴ If pipes will be opened together then they will fill 1/30 part of tank in 1 hour.

Now,

To get time to fill the full tank if both will be opened together then we have to divide by 1 to part of tank filled in w hour.

=> They take time to fill full tank = 1÷ 1/30

=> 1× 30/1

=> 30 hours

∴ If both pipes are opened together then they

will take 30 hours to fill the tank.