There are 3 pipes connected to the pool. Through one pipe, all the water flows out after 10 hours, the second pipe fills

There are 3 pipes connected to the pool. Through one pipe, all the water flows out after 10 hours, the second pipe fills the entire pool in 6 hours, the third fills in 4. What part of the pool will be filled in 1 hour if you open all pipes at the same time?

Let’s designate the volume of the pool given to us per unit. Since the first pipe fills it in 10 hours, then in an hour it will fill the pool for:

1: 10 = 1/10 (of the pool volume)

According to the condition, the second pipe fills the pool in 6 hours. It means that in an hour it will fill

1: 6 = 1/6 (of the pool volume)

Also, the third treasure fills the pool in 4 hours. Let’s find the volume that it will fill in an hour.

1: 4 = 1/4 (by volume)

Now we will find what volume all three pipes will fill together in an hour.

1/10 + 1/6 + 1/4 = 7/50 + 1/6 = 92/300 = 23/75