how Long does it take to fill the tank

Question

One pump fills a tank in 9 hours. A second pump fills the same tank in 6 hours. when a third pump is added and all three are used to fill the tank, it takes only 3 hours. find how long it takes the third pump to fill the tank

Answer 1

Let's name the first pump A, and the second pump B, and the mystery pump C. If we turn these English words into math phrases, we would write something like this:

A is 1 tank/9 hours and B is 1 tank/6 hours. We can use ideas from other rate units we've seen in real life, like miles per gallon, or meters per second. This makes C's unit 1 tank/?? hours. Now let's use the other information we're given in the problem. It says that all three pumps working at the same time fills the tank in 3 hours. That means we need to add all these rates together to solve for our mystery pump. We also need to make sure to compensate for the fact that three pumps are working at the same time, so they only need to fill a third of the tank.

3 hours = 1/3 tank per 3 hours + 1/3 tank per 2 hours + 1/3 tank per ?? hours. 

If you set up this equation and solve carefully for ??, you should get something that is much greater than 9. Remember to convert your answer back to the "1 tank" unit by multiplying your answer by 3. 

Answer 2

In three hours:

The first pump fills 3/9, or 1/3 of the tank.

The second pump fills 3/6, or 1/2 of the tank

That leaves 1/6 of the tank to be filled by the third pump

 

3/x = 1/6

3 = x/6

18 = x

 

The third pump would need 18 hours to fill the tank.