one pipe fills a store pool in 12 hours. A second pipe fills the same pool in 6 hours. When a third pipe is added and all three are uset otill the pool, it only takes 3 hours. Find how long it takes the third pipe to do the job

x = 12 hours

Step-by-step explanation:

If one pipe fills store pool in 12 hours in 1 hour will fill 1/12 of the pool

If one pipe fills a store pool in 6 hours in 1 hour will fill 1/6 of the pool

Let call " x " number of hours needed by the third pipe to fills the pool

then in 1 hour will fill 1/x

The three pipes working together in 1 hour will fill

1/12 + 1/6 + 1/x

Now we know that the three pipes take 3 hours to fill the pool then in 1 hour three pipes will fill 1/3 of the pool, therefore

1/12 + 1/6 + 1/x = 1/3

(x + 2*x + 12) / 12*x = 1/3 ⇒ (3*x + 12) / 12*x = 1/3

9*x + 36 = 12*x

- 3*x = - 36

x = 36/3

x = 12 hours