Question

A barrel contains 189 gallons of water and is being drained at a constant rate of 5 gallons per hour. Write an equation that models the number of gallons g, after t hours. Can anyone help me with this equation, or an example of one similar?

Answer 1

At the beginning, when t = 0, g = 189

Answer 2

As time goes by, when
t = 1, it lost 5 gallons times 1, or -5 gallons
t = 2, it lost 5 gallons times 2, or -5 * 2 = -10 gallons
t = t, it lost 5 gallons times t, or -5t gallons
The expression is the original amount plus the loss:
g = 189 - 5t

Answer 3

To check to see if this expression is correct, substtitute a few values of t and evaluate it.

At t = 0, no water has drained, so it should have the full 189 gallons:
g = 189 - 5(0) = 189 - 0 = 189

After 1 hour, at t = 1, it lost 5 gallons, so it has 189 - 5 = 184:
g = 189 - 5(1) = 189 - 5 = 184

It looks like
g = 189- 5t
is the correct expression.

Answer 4

I see... That makes sense! Thank you very much. I wasn't sure how to do this, but that makes a lot of sense now. Thank you, thank you!

Answer 5

You're welcome.

Answer 6

one sec-

Answer 7

when you were figuring it out, after you wrote t=1, t=2,etc., you wrote t=t, it lost 5 gallons times t or -5 gallons..

Answer 8

is that just the expression w/out plugging in an amount for t?

Answer 9

t is the general term for t number of hours.
That's how we get the -5t part of the expression.
In 1 hour it looses 5 gal
In 2 hours it looses 10 gal
In 3 hours it looses 15 gal
In t hours it looses 5t gal

Answer 10

oh, ok. Duh me!! LOL thanks!