Question

A 20 000 L tank drains at a constant rate. It takes 100 min to empty the tank. When is there 6 000 L of liquid left in the tank?

Answer 1

Answer: 70 minutes

===================================================

Explanation:

x = time in minutes

y = amount of water left in thousands (eg: y = 4 means there's 4000 liters of water left)

The point (0,20) means that at the starting point 0 minutes, the tank has 20 thousand liters of water in it

The point (100,0) indicates that after 100 minutes, there is no water left

Find the slope of the line through those points (see the attached figure below). This slope is m = -1/5 = -0.2

The y intercept is b = 20 because the initial amount of water in the tank is 20 thousand liters.

Therefore, the equation of the line goes from y = mx+b to y = -0.2x+20

The last step is to plug in y = 6 and solve for x

y = -0.2x+20

6 = -0.2x+20 ...... replace y with 6

6-20 = -0.2x+20-20 .... subtract 20 from both sides

-14 = -0.2x

-0.2x = -14

-0.2x/(-0.2) = -14/(-0.2) ..... divide both sides by -0.2

x = 70

It takes 70 minutes to have 6000 liters left in the tank.