Question

How many gallons per minute leak out of container B?
Graph:
points 400 , 25and 100, 50
going down

Answer 1

To determine how many gallons per minute leak out of container B, we will need to analyze the coordinates you provided: (400, 25) and (100, 50).

From these points, it seems that you're describing a linear relationship between time (on the x-axis) and the volume of liquid remaining in container B (on the y-axis).

To find the leak rate in gallons per minute, we can find the slope of the line represented by these two points. The slope \((m)\) can be calculated using the formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

With your points:
- Point 1: \( (x_1, y_1) = (400, 25) \)
- Point 2: \( (x_2, y_2) = (100, 50) \)

Now we plug in those values:

\[
m = \frac{50 - 25}{100 - 400} = \frac{25}{-300} = -\frac{1}{12}
\]

The negative sign indicates that the volume is decreasing over time, which fits with the context of a leak.

Now, since the slope represents the change in gallons per minute, we convert it to a leak rate:

\[
\text{Leak rate} = -m = \frac{1}{12} \text{ gallons per minute}
\]

This means that container B is leaking approximately **0.0833 gallons per minute** (or 1/12 of a gallon per minute).