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

[mathdad]

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.

 

[mathdad]

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!

 

[mathdad]

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?

 

[MarkFL]

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:

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

 

[mathdad]

Correct.
Yes.

(15/8)(2/3) = 5/4 hrs

 

[Wilmer]

Stick a pink star on your forehead :)