## ShotGunGirl 3 years ago This is really hard D8 A tank can be filled by one pipe in four hours and by a second pipe in six hours; and when it is full, the tank can be drained by a third pipe in three hours. If the tank is empty and all three pipes are open, in how many hours will the tank be filled? 8 hours 12 hours 24 hours

1. jabberwock

You have that the first pipe can fill the tank in 4 hours. This means that it fills the tank 1/4 full each hour. Suppose we have x hours. After x hours, it is filled to (1/4)*x. We can test this by looking at how full it should be after 4 hours. (1/4)*4 = 1, or one full tank. The second pipe will fill after 6 hours, which means it fills 1/6 of the tank every hour. So we have 1/6x as the height of the tank if only the second pipe is turned on. Add both of these together to get $\frac{1}{4}x+\frac{1}{6}x$as the amount of water entering the tank. The amount of water leaving the tank is (1/3)x, because it takes three hours to drain a full tank. We want to know how much time it takes to fill the tank. In other words, we want 1 full tank. So the left side of the equation will look like 1=... The entire equation should look like this: $1=\frac{1}{4}x+\frac{1}{6}x-\frac{1}{3}x$ If you remember your fractions, you should be able to solve for x from there.

2. ShotGunGirl

Thank you<3

3. jabberwock

Sure thing :) . Did that make sense?

4. ShotGunGirl

Perfect sense. Thank you again.