Question

The summer has ended and it's time to drain the swimming pool. 20 minutes after pulling the plug, there is still 45 000L of water in the pool. The pool is empty after 70 minutes. Calculate the rate that the water is draining out of the pool. b) Calculate how much water was in the pool initially. c) Write an equation for this relationship. d) Use your equation to calculate how much water is in the pool at 62 minutes.

Answer 1

a) -900 L/min

b) 63000 L

c) -900t +63000

d) 7200 L

Explanation:

a) You are given two points on the curve of volume vs. time:

(t, V) = (20, 45000) and (70, 0)

The rate of change of volume

= ΔV/Δt = (0 -45000)/(70 -20) = -45000/50 = -900 liters per minute

b) In the first 20 minutes, the change in volume was

(20 min)(-900 L/min) = -18000 L

So, the initial volume was

initial volume - 18000 = 45000

initial volume = 63,000 liters

c) Since we have the slope and the intercept, we can write the equation in slope-intercept form as

V= -900t +63000.

d) now putting the number in the equation and do the arithmetic.

When t=62, the amount remaining is

= -900(62) +63000 = -55800 +63000 = 7200

Thus, 7200 L remain after 62 minutes.