In pipes and water tank we will learn how to solve different types of problems. A water tank or a cistern is connected with two types of pipes to fill and empty it. The pipe which fills the tanks up is called the inlet. The pipe which empties it is called the outlet.
Suppose, if an inlet fills up the cistern in 5 hours, then in 1 hour it fills up 1/5 th part of it. We say that the work done by inlet in 1 hours is 1/5.
Similarly, if an outlet empties out the cistern in 4 hours, then in 1 hour it empties out 1/4 th part of the cistern. We say that the work done by the outlet in 1 hour is 1/4.
Now we will apply the concept of solving some real-life problems on pipes and a water tank or a cistern.
Word problems on pipes and water tank or cistern:
1. A cistern can be filled by a tap in 5 hours by the other tap in 4 hours. If both taps are opened together how long will it take to fill the cistern?
Time taken by the 1st tap to fill the cistern = 5 hours
Therefore, work done by the 1st tap in 1 hour = 1/5
Time taken by the 2nd tap to fill the cistern = 4 hours.
Therefore, work done by the 2nd tap in 1 hour = 1/4
Therefore, work done by the both taps in 1 hour = 1/4 + 1/5
= (4 + 5)/20
Therefore, both taps will fill the cistern in = 20/9 hours.
2. A tank can fill by the taps in 8 hours and can be emptied by the other taps in 10 hours. How long will it take to fill the tank if both the taps are opened together?
Time taken by the 1st tap to fill the tank = 8 hours
In 1 hour, the tap fills 1/8 of the tank.
Time taken by the other tap to empty the tank = 10 hours
In 1 hour, the other tap empty -1/10 of the tank (since, empty is taken as negative)
Therefore, in 1 hour work done by tap A and tap B = 1/8 – 1/10
= (5 – 4)/ 40
Therefore, both the taps when opened together will fill the tank in 40 hours.
3. A tank can be filled by one tap in 4 hour and empty by an outlet pipe in 6 hours. How long will it take to fill the tank if both the tap and pipe are opened together?
Time taken by tap to fill the tank = 4 hours
In 1 hour, the tap fill 1/4 th part of tank.
Time taken by pipe to empty the tank = 6 hours
In 1 hour, the pipe empties 1/6 th part of the tank.
Thus, in one hour (1/4 – 1/6) th = (3 – 2)/12) th
= 1/12 th part of the tank is filled.
Therefore, the tank will be filled in 12 hours.