There is a water tank with a drain of an unknown size that is always open. There is a series of input pipes above it which are all the same size. When 4 pipes are on, it takes 6 hours to fill. When 3 pipes are on, it takes 10 hours to fill. How many pipes would it take to fill the tank in 3 hours?

Question

There is a water tank with a drain of an unknown size that is always open.  There is a series of input pipes above it which are all the same size.  When 4 pipes are on, it takes 6 hours to fill.  When 3 pipes are on, it takes 10 hours to fill.  How many pipes would it take to fill the tank in 3 hours?

Steve · Answer

if an input pipe could fill the tank in x hours, and the drain could empty it in y hours with no input,

4/x - 1/y = 1/6
3/x - 1/y = 1/10

x=15,y=10

so, if n pipes fill the tank in 3 hours,

n/15 - 1/10 = 1/3
n = 13/2

Hmmm. I was expecting an integer.

Jimmy · Answer

Could you help explain how T can put the number of pipes over the time to solve this?? I'm afraid I don't understand.