Question

one pipe fills in 4 hrs and another in 5hrs when they both work alternately how much time will be taken to fill the tank.

Answer 1

So, Let Pipe A Fill in 4 hrs and Pipe b fill in 5 hrs.
Pipe A Fills the whole Volume in 4 hrs.
So Pipe A Can Fill 1/4 of the total Volume in An Hour.
Similarly,Pipe B Can Fill 1/5 Of The Total Volume.
So In 2 Hour Both Of The Pipes Together Fill 1/4 +1/5 of the total Volume.
2hr = 9 /20. of the volume
So Total hours would Be 40/9
That is 4.44 Hrs.
This Is The The Solution To The Given Question.

Answer 2

Let pipe1 be x and pipe 2 be y. It is difficult to write pipe 1 and pipe 2 always.


Given that work was done by x in an hour = 1/4.

Given that work was done by y in an hour = 1/5.

If x and y work alternately, then the work done by them in 2 hours

= (1/4 + 1/5)

= 9/20.


Then the work was done by them in 4 hours if they work alternately

= 2(9/20)

= 18/20

= 9/10.


Then the Remaining part = 1 - 9/10

                                           = 1/10.


Now,

1/10th part of the tank is filled by x in (1/10) * 4

                                                             = 4/10

                                                             = 2/5 hours

                                                             = 0.4 hours

                                                             = 24 minutes.


Therefore, the total time is taken to fill the tank = 4 hours 24 minutes.


Hope this helps!