# If both are used together, how long will it take to fill the empty tanker of an oil tanker that is filled in 4 hours by one pipe; another pipe to empty the tanker takes 6 hours.

jeew-m | Certified Educator

Let the volume of the tank is `V m^3` .

Then;

The rate of filling (input)= V/4 `m^3/h`

The rate of emptying (out put) = `V/6 m^3/h`

So;

input rate = V/4 `m^3/h`

Output rate = V/6 `m^3/h`

When both are working simultaniously;

Net input rate = input rate - output rate

= V/4-V/6 `m^3/h`

= V/12 `m^3/h`

So the rate of filling the tank is `V/12 m^3/h` .

So the time to fill = Volume /rate of filling

= `V/(V/12)`

= 12 h

So it ill take 12 hours to fill the tank.

justaguide | Certified Educator

An oil tanker can be filled by pipe A in 4 hours. The pipe fills the tanker at the rate of 1/4 per hour. The tanker can be emptied by pipe B in 6 hours. It is emptied at the rate of 1/6 per hour.

If the two pipes are used together, the rate at which the tanker is filled is 1/4 - 1/6 = 1/12

The time taken to fill an empty tanker at this rate is 12 hours.

It would take 12 hours to fill an empty tanker if both the pipes are used together.

vaaruni | Student

Since In 4 hrs. a pipe (A) fills a tan

Therefore In 1 hr. it will fill 1/4  of a tank.

In 6 hrs. another pipe(let B) empties the tank

Therefore in 1hr. the pipe(B) will empty 1/6 of a tank

If both the pipes(A & B) are on then ,

in 1 hr  {(1/4) - (1/6)  } of the tank will be filled

1/4 -1/6 = (3 - 2)/12 = 1/12

Therefore in 1 hr. both pipes will fill 1/12 of the tank.

Since 1/12 of the tank is filled in 1 hr. when both pipes are on.

Therefore 1 tank will bw filled in 12 hrs.

It will take 12 hrs. to fill empty tanker if both pipes are used <- Answer