The time requir

Question

The time required for an outlet pipe to empty a tank is inversely proportional to the​ cross-sectional area of the pipe. A pipe with a​ cross-sectional area of

113.0113.0

sq in. requires

6.2 hours6.2 hours

to empty a certain tank. If the pipe was replaced with one with a​ cross-sectional area of

53.2553.25

sq​ in., how long would it take this pipe to empty the same​ tank?

A pipe with a​ cross-sectional area of

53.2553.25

sq in. would take

nothing

hours.

Answer 1

In the problem, it says the cross-sectional area (basically, how big the opening of the pipe is) is inversely (opposite) proportional to the time it takes to empty the tank. This makes sense. If the opening is super big, it will hardly take any time to empty the tank. If the opening is really tiny, it will take forever to empty the tank.

Let's write what we just said above as an equation:

Cross-sectional area = (Constant of Proportionality) / (Time to empty the tank)

Let's call the constant of proportionality k. That's basically just the ratio between how big the opening is and how long it will take to empty the tank. It has to do with how fast water flows.

To answer this problem, the first step is to find k. We have enough information from the first scenario to do this. Let's plug the information from the first scenario into the equation we wrote above:

113sq.in = k/ (6.2 hrs)

k= 113sq.in x6.2hr = 700.6sq.in-hr

Now that we know what k is, and we know how big the opening is in the second scenario, we can find out how long it will take!

53.25 sq.in = 700.6 sq.in-hr / (# of hours to empty the tank)

Now, just solve for the number of hours to empty the tank!