The local zoo has two water tanks for the elephant exhibit that are leaking One water tank contains 12 gal of water and is leaking at a constant rate of 3 gal/h. The second water tank contains 8 gal of water and is leaking at a constant rate of 5 gal/h. When will the two tanks have the same amount of water? Explain. Let x = the number of hours the tanks are filling and let y = the number of gallons in the tank.

Question

anonymous · Answer

A. In 2 hours, because the solution to the system is (2,18).	

B. They will never have the same amount of water because the solution to the system is (–2,18). It is not possible to have time be –2 hours.	

C. In –2 hours, because the solution to the system is (–2,18).	

D. They will never have the same amount of water because the solution to the system is (–2,18). It is not possible to have –2 gallons in the tanks.

anonymous · Answer

I believe it is A.. am I correct?

anonymous · Answer

I used substitution...

missmob · Answer

i think it a

anonymous · Answer

great, thanks!

missmob · Answer

no prob

anonymous · Answer

I got it incorrect!

anonymous · Answer

:'(

missmob · Answer

hey it like there will never have same amout

anonymous · Answer

so, it must be D? Because y is the number of gallons?

missmob · Answer

yes

whpalmer4 · Answer

First tank contains $F = 12-3t$ gallons where $t$ is number of elapsed hours
Second tank contains $S = 8 - 5t$ gallons
Set the two equal to each other and solve for $t$, or graph both and find the point of intersection.

$$F = S$$$$12-3t=8-5t$$$$4=-2t$$$$t=-2$$The only time the tanks have the same amount of water is outside the domain of the problem, so the answer must be D.

anonymous · Answer

Thanks so much for an EXPLANATION! I appreciate it!

whpalmer4 · Answer

You're welcome.  I think just giving an answer gives about as much help as if we simply guessed, so not much point, right? :-) [In my experience, the people who reply with just answers instead of showing how to get them are more likely to be incorrect, too!]

whpalmer4 · Answer

Here's a bit of a challenge for you: suppose the problem had one of the tanks both leaking and being filled at the same time.  Do you think, armed with my example, that you could figure out how to write the equation showing the amount of water in the tank?