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3 Pumps Working 8 Hours a Day Can Empty a Tank in 2 Days. How Many Hours a Day Must 4 Pumps Work to Empty the Tank in One Day?

  • 3 pumps working 8 hours a day can empty a tank in 2 days.
  • Hours that 4 pumps require to empty the tank in one day can be figure out in this way.

Explanation

Three given entities here are

  1. Pump
  2. Days
  3. Hours

To determine the relation here, let suppose; Hours that 4 pumps require to empty the tank in one day = y

Case I

Pump         Hours

3                 8

4                 y

  • Lesser pumps mean more time that would require more hours.
  • More pumps mean less time.

This clearly indicates that there is inverse relation.

Direct/Indirect relation tells how the equation will be written.

3 : 4  ::  y : 8 ________ (i)

Case II

Days           Hours

2                 8

1                 y

  • More days mean less hours.
  • Less days mean more hours.

This clearly indicates that there is also inverse relation.

Direct/Indirect relation tells how the equation will be written.

2 : 1  ::  y : 8 ________ (ii)

By (i) and (ii)

3 : 4 :: y : 8

     2 : 1

3 x 2 x 8 = 4 x 1 x y ________ (A)

After simplifying equation (A), we can easily figure out the value of y (y = 12 hours)

To Find

Hours that 4 pumps require to empty the tank in one day = ?

Solution

Method I

Let suppose

Hours that 4 pumps require to empty the tank in one day = y

Pump         Days           Hours

3                 2                 8

4                 1                 y

  • Relation between pump and hours is inverse.
  • Relation between days and hours is also inverse so;

3 : 4 :: y : 8

     2 : 1

3 x 2 x 8 = 4 x 1 x y

48 = 4y

4y = 48

y = 48/4

y = 12 hours

Hours that 4 pumps require to empty the tank in one day = 12 hours answer

Method II

Hours that 3 pumps require to empty the tank in 2 days = 8 hours

Hours that 3 pumps require to empty the tank in 1 day = (8 x 2) hours

Hours that 1 pump require to empty the tank in 1 day = (8 x 2 x 3) hours

Hours that 1 pump require to empty the tank in 1 day = 48 hours

Hours that 4 pump require to empty the tank in 1 day = 48/4 hours

Hours that 4 pump require to empty the tank in 1 day = 12 hours

Hours that 4 pumps require to empty the tank in one day = 12 hours answer

Conclusion

3 pumps working 8 hours a day can empty a tank in 2 days. 12 hours a day must 4 pumps work to empty the tank in one day.

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