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Solution to Puzzle 43.  FILLING A TANK

A large gasoline tank has three inlet pipes and one outlet pipe.  One inlet pipe, colored red takes 2 hours to fill the tank.   Another inlet pipe, colored blue, takes 3 hours to fill the tank.  The third inlet pipe, colored green, takes 4 hours to fill the tank.  The outlet pipe empties the whole tank in 12 hours.

If the tank is initially empty, how long would it take to fill the tank if all the pipes are fully in operation?


The rates for the pipes are:

red pipe = 1/2 tank per hour
blue pipe = 1/3 tank per hour
green pipe = 1/4 tank per hour
outlet pipe = -1/12 tank per hour

1 full tank = rate x time
1 = (1/2+1/3+1/4-1/12) time
time = 1 hour

Therefore, it would take 1 hour to fill up the tank.

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