Write a function S(t), that models how many gallons of sauce are in the tank after t hours.

Question

You are a pizza place owner and to put sauce on the pizza you have robot names Saucebot. All you have to do is keep track of Saucebot's sauce tank and make sure it doesn't go empty. After 1 hour of work, there are 45 gallons left in the tank. After 3.5 hours, there are 20 gallons of sauce left. After how long will you need to fill his tank up? What are the units for the slope? What does this tell you about your robot?

Answer 1

Josh,

Remember that slope is determined by the change in y divided by the change in x. In this case, time is the independent variable and so is represented by x. This leaves the gallons of sauce as y. Our two data points are (1, 45) and (3.5, 20).

 

so slope (m) = (y₂ - y₁)/(x₂ - x₁) = (20 - 45)/(3.5 - 1) = -25/2.5 = -10

 

This tells us that the robot applies 10 gallons of sauce per hour.

 

To find the time until reloading, we need to know the total volume. For that, we'll write the equation of the line.

 

y - y₁ = m(x - x₁)           general point slope form

y - 45 = -10(x - 1)           distribute the -10 and add 45

y = -10x + 10 + 45         combine like terms

y = -10x + 55

 

This tells us that the robot holds a total of 55 gallons of sauce.  So if vol/rate = time,

 

55 / 10 = 5.5 hours until reload is necessary.