A swimming pool can be filled by one pump in 36 minutes and by another pump in 54 minutes. A third pump can drain the pool in 108 minutes. If all 3 pumps go int

Question

Please tell me how to solve this problem thanks 

Answer 1

Let x = amount of time that it takes to fill the tank if all three pumps are working

 

1/36 = portion of pool filled by the first pump per minute

 

1/54 = portion of pool filled by the second pump per minute

 

1/108 = portion of pool emptied by the third pump per minute

 

1/x = portion of pool filled by all 3 pumps per minute

 

1/36 + 1/54 - 1/108 = 1/x

 

Multiply through by the LCD, 108x, to get:  3x + 2x - x = 108

 

                                                                           4x = 108

 

                                                                            x = 27 minutes