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

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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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