A tank contains 24 gallons of water when all of a sudden the water begins draining at a constant rate of 2 gallons per hour. Let

Question

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A tank contains 24 gallons of water when all of a sudden the water begins draining at a constant rate of 2 gallons per hour. Let

t represent the number of hours since the water began draining and let v represent the volume of water in the tank.
Required:
a. Write a formula that expresses v in terms of t.
b. As t increases from 3 to 6, v varies from _________ to _________

Mathematics

1 answer:

AnnZ [12.3K] · Answer 1 · 2026-02-23T23:09:51+03:00

Response:

a) $V(t) = 24 - 2t$

b) From t increasing from 3 to 6, v changes from 18 gallons to 12 gallons.

Detailed explanation:

The relationship between the tank’s volume and time is given by:

$V(t) = V(0) - at$

Where V(0) indicates the starting volume and a denotes the hourly decrease.

a. Create a formula for v in terms of t.

The tank starts with 24 gallons of water, hence $V(0) = 24$

It drains steadily at 2 gallons each hour, therefore $a = 2$

Then

$V(t) = V(0) - at$

$V(t) = 24 - 2t$

b. When t progresses from 3 to 6, v changes from _________ to _________

$V(t) = 24 - 2t$

$V(3) = 24 - 2*3 = 18$

$V(6) = 24 - 2*6 = 12$

So as t progresses from 3 to 6, v shifts from 18 gallons to 12 gallons.