Question

Rain is flowing into two containers at

different rates. The figure below shows the
volume of water in each container at
different times.
What is the difference in the rate of change between the two containers?

A.1/5 gallon per minute
B.3/5 gallon per minute
C.5/2 gallon per minute
D.15/2 gallon per minute

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=(y_2-y_1)/(x_2-x_1)`

`$m=(4-2)/(20-10)`

`$m=(2)/(10)`

`$m=(1)/(5)`

Rate of change for container 1 is
`(1)/(5)`.

Take any two points on container 2.

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

`$m=(y_2-y_1)/(x_2-x_1)`

`$m=(4-2)/(10-5)`

`$m=(2)/(5)`

Rate of change for container 2 is
`(2)/(5)`.

Difference =
`(2)/(5)-(1)/(5)`

`$=(1)/(5)`

The difference in the rate of change between the two containers is
`(1)/(5)` gallon per minute.