word problems

Question

One pipe takes 6hours to fill a tank, and another pipe empties it in 8hours.  If both pipes are open, how many hours will it take to fill the tank

Answer 1

Let x = number of hours to fill the tank if both pipes are open

 

1/6 = portion of tank filled per hour by the first pipe

1/8 = portion of tank emptied per hour by the second pipe

1/x = portion of tank filled per hour if both pipes are open

 

Then, 1/6 - 1/8 = 1/x

 

Multiply by the LCD, 24x:  4x - 3x = 24

 

                                              x = 24 hours