Chapter 7.8, Problem 20P

To determine

Tofind:the duration of pipe to fill the empty half-filled tank.

Answer to Problem 20P

If both pipes are accidentally opened it will take $\text{2}$ hours to fill the empty a half- filled tank.

Explanation of Solution

Given:

The fill pipe for tank can fill the tank in $\text{4}$ hours.

The drain pipe can drain it in $\text{2}$ hours.

Concept used:

Rate of the work:

Ratio of work to the time interval with changes in time rate of work will change.

  $\text{work rate=}\frac{\text{work done}}{\text{time}}$ .

  $\text{work rate}\times \text{time=workdone}$ .

Calculation:

The equation where $\text{x}$ is the amount of time both are open.

Remember since one pipe is draining the tank so, work done by that pipe is subtracted. also, the equation equals negative one half instead of 1 since the tank is half- filled and is being drained, not filled.

  $\frac{\text{x}}{4}-\frac{\text{x}}{\text{2}}\text{=-}\frac{\text{1}}{2}$ .

Multiplying, both sides by the L.C.D of $\text{4}$ .

  $\text{x-2x=-2}$ .

  $\text{-x=-2}$ .

Multiplying both side by $\text{-1}$ .

  $\text{x=2}$ .

Hence if both pipe are accidentally opened it will take $\text{2}$ hours to fill the empty a half filled tank.