Bathtub Problem

Bathtub Problem
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  • Yeah, it seemed like it was acting funny. Well, I know that at one point the tub had been draining for 40 seconds and had 13 gallons of water. Then at another point had been draining for 60 seconds and had 10 gallons of water left in it.
  • So you said that it seemed like it was draining weird when you unplugged it? I'm going to need a little more information in order to fix it.
  • In order to fix the tub, I need to supply the plumber with more information, and I don't know what to do.
  • Honey, are you OK? You seem a little stressed about something. 
  • I'll make it simple for you. Since you already have some information, use those to figure it out. It's almost like a linear equation. You'll make it work.
  • So, with what I have so far I figured out that the tub loses 3 gallons of water every 20 seconds.
  • Well, I have two different pieces of information. The amount of time the tub has been draining, and the amount of water in the tub. 
  • This means that by y-intercept would be 19 gallons because that's how many gallons there were in the tub before it started draining.  So, my x-intercept is approximately 126 seconds because that's how long it would take the tub to drain completely.
  • I know that gallons would be my y value and the amount of time would be my x value. 
  • Since I have figured out all of the information I needed to know, I was able to figure out that after 20 seconds there will be 16 gallons left in the tub. But after 50 seconds there will only be 11.5 gallons left.  I almost forgot that I also figured out that when there are 7 gallons left in the tub, it would have been draining for 80 seconds.
  • See! I knew you could do it! Now you have enough information to give to the plumber.
  • Yes, I did actually. The amount of gallons of water is equal to how much water you started with, plus the rate at which the tub drains multiplied by how long the tub had been draining. 
  • Did you end up figuring out the information I need to fix the drain?
  • Well, that is some really good news. Mainly because I can fix your tub and finally get paid now!
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