A full 1,500-liter water tank springs a leak and is losing 2 liters per minute. A second tank has 300 liters and is being filled at a rate of 6 liters per minute.

1. Will the first or second tank have more water after 170 minutes?
2. At what point will both tanks have the same amount of water?

Question

High School

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Answer :

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FarzaLC FarzaLC · Answer 1 · 2024-11-03T23:25:33-05:00

Final answer:

Explanation:

To solve this problem we need to create equations that represent the amount of water in each tank over time.

Let's denote the amount of water in the first tank as A1 and the second tank as A2. After t minutes:

A1 = 1500 - 2t

A2 = 300 + 6t

-For the first part of the question, to figure out which tank will have more water after 170 minutes, substitute t=170 into these equations:

A1 = 1500 - 2(170) = 1160 liters

A2 = 300 + 6(170) = 1320 liters

So, the second tank will have more water.

-For the second part of the question, both tanks will have the same amount when A1 = A2.

So, set the two equations equal to each other and solve for time:

1500 - 2t = 300 + 6t

1200 = 8t

t= 150

Solving gives t =150 minutes.

So, after 150 minutes, both tanks will have the same amount of water.

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