Answer to Question #87822 in Calculus for Piper

Question

To pump water into the pool more quickly, six machines are used, though all machines are not started at the same time. The function:

p(t)=w(t)+w(t−2)+w(t−4)+w(t−9)+w(t−16)+w(t−30),fort⩾0

represents the total number of gallons pumped by all of the machines after t minutes of the first machine beginning to operate.

C) Using the definition of p(t), how many of the machines are have been turned on 10 minutes after the first pump is turned on?
The number of machines that are on 10 minutes after the first pump is turned on is equal to

Answer 1

Fot t=10 minutes

$$p(t)=w(t)+w(t-2)+w(t-4)+w(t-9)+0$$

After 10 minutes of the first machine beginning to operate:

first machine works during 10 minutes;

second machine works during 8 minutes;

third machine works during 6 minutes;

fourth machine works during 1 minute.

The fifth and sixth machines are not started yet.

The number of machines that are on 10 minutes after the first pump is turned on is equal to 4.