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Leokris [45]
3 years ago
7

A large container holds 5 gallons of water. It begins leaking at a constant rate. After 20 minutes, the container has 3 gallons

of water left. At what rate is the water leaking? Express your answer as a positive value.
Mathematics
1 answer:
jeka57 [31]3 years ago
4 0

The container will take 25 minutes to go from full to empty.

Explanation:

In 15 minutes, the container has lost 3 gallons of water (

5

−

2

=

3

).

Since the leak is at a constant rate, we can determine that every five minutes the container loses one gallon.

So for the container to lose the full 5 gallons will take 25 minutes (

5

×

5

=

25

)

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Let

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In order to prove this by induction, we first need to prove the base case, i.e. prove that P(1) is true:

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So, the base case is ok. Now, we need to assume P(n) and prove P(n+1).

P(n+1) states that

P(n+1):\ 1+2+\ldots+n+(n+1) = \dfrac{(n+1)(n+2)}{2}=\dfrac{n^2+3n+2}{2}

Since we're assuming P(n), we can substitute the sum of the first n terms with their expression:

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Which terminates the proof, since we showed that

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3 years ago
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Answer:

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