I am trying to figure out how an answer from my textbook was worked out. The textbook contains MANY ridiculous errors, so I would like to get a second opinion from someone here regarding the accuracy of the solution. It is possible that I just do not understand the logic, but I want to be sure before I go wasting any more time on it. Here is the question:
The solution provided is as follows:
A plastic juice bottle holds 2 L of liquid. In an experiment, a small hole is drilled in the bottom of the bottle. The volume of liquid, V, remaining after t seconds can be modelled by V(t) = 2 - t/5 + t^2/200, where t >= 0. How long does it take for the 2L of liquid to drain from the bottle?
I do not understand how they are getting to step #2 in their solution and I would really appreciate some clarification. I have been racking my brain all day on other problems so it is possible I am overlooking something really obvious at this point.
V(t) = 2 - t/5 + t^2/200
V(t) = 2000 - 200t + 5t^2
V(t) = 5(400 - 40t + t^2)
V(t) = 5(20 - t)(20 + t)
20 - t = 0
20 = t
It takes 20 seconds to drain the bottle.