Question

Rain is flowing into two containers at

Answer 1

Given:

Volume of water in each container.

To find:

Difference in the rate of change.

Solution:

Take any two points on container 1.

Let the points are (10, 2) and (20, 4).

$m=\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{4-2}{20-10}$

$m=\frac{2}{10}$

$m=\frac{1}{5}$

Rate of change for container 1 is $\frac{1}{5}$.

Take any two points on container 2.

Let the points are (5, 2) and (10, 4).

$m=\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{4-2}{10-5}$

$m=\frac{2}{5}$

Rate of change for container 2 is $\frac{2}{5}$.

Difference = $\frac{2}{5}-\frac{1}{5}$

                  $=\frac{1}{5}$

The difference in the rate of change between the two containers is $\frac{1}{5}$ gallon per minute.