Question

The water depth in two ponds is measured annually.

The first depth measurement in the first pond is 22 feet.
The first depth measurement in the second pond is 32 feet.
Annual measurements show the first pond’s depth decreasing by 0.4 feet per year and the second pond’s depth decreasing by 0.8 feet per year.
This information can be represented by a system of equations, as shown below. In the equations, x is the time in years and y is the depth in feet.

 y=-2/5x+22

y=-4/5x+32

Assuming the rates of decrease are constant, how much time does it take for the depth of each pond to be the same?

Answer 1

Set the two equations equal and solve for x:

-2/5 x + 22 = -4/5 x + 32
(4/5 - 2/5) x = 32 - 22
(2/5) x = 10
x = 10 * (5/2) = 25

It takes 25 years. (At that time the depth in each pond will be 12 ft.)