# If both pipes are used together, how long will it take to fill 2/3 of the tank?

• MHB
One inlet pipe fills an empty tank in 5 hours. A second inlet pipe fills the same tank in 3 hours. If both pipes are used together, how long will it take to fill 2/3 of the tank?

My Work:

Let x = time when both pipes are used together

(1/5) + (1/3) = 1/x

I found x to be 15/8 hours.

Must I now multiply (15/8)(2/3)?

Wilmer
I found x to be 15/8 hours.

Must I now multiply (15/8)(2/3)?
Correct.
Yes.

Correct.
Yes.

It took several tries before I found the correct set up. Unfortunately, no such thing as ENOUGH TIME when taking a test.

HOI
That's why you "practice, practice, practice" before the test!

That's why you "practice, practice, practice" before the test!

My classroom days ended in December 1993.

HOI
Then what "test" were you talking about?

Wilmer
Test tickle?

Gold Member
MHB
As a slightly different way to approach this problem, we can see that working together for 15 hours, the two inlet pipes can fill 8 tanks, and so it would take 15/8 hours for the two pipes to fill one tank, and 2/3 of that time to fill 2/3 tank, since the two pipes flow presumably at constant rates. Hence:

$$\displaystyle t=\frac{2}{3}\cdot\frac{15}{8}\text{ hr}=\frac{5}{4}\text{ hr}$$