Question

2. A new pump is used to empty the pool in Exercise 1. The equation

W= -275(2t - 7) represents the gallons of water w that remain in
the pool t hours after pumping starts.
a. How many gallons of water are pumped out each hour?
b. How much water is in the pool at the start of pumping?
c. Suppose there are 1,000 gallons of water left in the pool. How long
has the pump been running?
d. After how many hours will the pool be empty?
e. Write an equation that is equivalent to w= -275(2t - 7). What
information does it tell you about the situation?

Answer 1

a. 550 gallons/hr.

b. 1925 gallons

c. 1.268 hours

d. 3.5 hours

Explanation:

W = -275(2t-7), where t is hours since pumping starts. Let's rewrite this in standard line format of y = mx + b, where m is the slope and b the y-intercept (the value of y when x = 0). In this case we'll use W and t instead of x and y.

W = -275(2t-7)

W = -550t + 1925

The 1925 figure represents the water volume when t = 0, the initial volume. The slope of -550 is the rate at which water is being pumped out. 550 gallons/hr.

We can solve the equation for the hours required to make w=0:

W = -550t + 1925

0 = -550t + 1925

550t = 1925

t = 3.5 hours

-

We can solve for when W = 1,000:

W = -550t + 1925

1000 = -550t + 1925

-925 = -550t

t = 1.682 hours

a. 550 gallons/hr.

b. 1925 gallons

c. 1.268 hours

d. 3.5 hours

We can also graph the function. attached.