Question

PLEASE HELP:
A barrel contains 160 gallons of water and is being drained at a constant rate of 7 gallons per hour.
Write an equation that models the number of gallons, g, after t hours.

Answer 1

@whpalmer4

Answer 2

Initial contents = 160 gallons. This is a simple rate problem: v = rt, where v is the volume drained, r is the rate of draining (7 gal/hr) , and t is the amount of time that has passed. Your equation will take the initial contents and subtract the amount that has drained. What do you think it is?

Answer 3

22.85? @whpalmer4

Answer 4

Is 22.85 an equation modeling the number of gallons, g, after t hours?

Answer 5

huh?????? @whpalmer4

Answer 6

You have to read the question carefully, and answer what it asks. It doesn't ask how many hours it will take to drain the barrel.

Answer 7

You did a great job of answering that question (well, you didn't include the unit), but that wasn't what they asked for!

Answer 8

do i just write an equation? @whpalmer4

Answer 9

What part of "Write an equation that models the number of gallons, g, after t hours." isn't making sense to you?

Answer 10

is it 160=7t @whpalmer4

Answer 11

No. Look, the amount in the barrel is 160 gallons at t = 0, right? After that, some number of gallons drains out, the amount being found by v = rt where r = 7 gal/hr and t is the number of hours.

Answer 12

160 = 7t makes no sense when you plug in a number of hours. 160 = 7 * 1 hours? Fails both numerically and dimensionally.

Answer 13

i still dont understand=(...... im sorry im just really tired it 12 in the morning so im not understanding this as much @whpalmer4

Answer 14

A valid equation will have valid units for the results. For example, the v = rt equation has gallons on the left = gallons/hour * hours on the right, so we have gallons = gallons

Answer 15

Amount in the barrel at the start is 160 gallons. So at t =0, our equation to show how much remains in the barrel is simply:

W = 160 gallons.

If we let water drain out for 1 hour, the barrel will lose (7 gallons/hr)(1 hr) = 7 gallons
and will now contain 160-7 gallons = 153 gallons.

After another hour, the barrel will have lost (7 gallons/hr)(2 hr) = 14 gallons and will now contain 160-14 = 146 gallons.

Do you see the pattern?

After we open the drain, and 7 gallons/hour starts pouring out, the barrel will contain
W = 160 gallons - (7 gallons/hour)t where t is in hours. Let's check it out:

at t = 0,
W = 160 gallons - (7 gallons/hour)(0 hours) = 160 gallons

at t = 22.85 hours
W = 160 gallons - (7 gallons/hour)(22.85 hours) = 0 gallons

Answer 16

so the equation is W= 160-(7g/h)(0h)=160? @whpalmer4

Answer 17

No. Do you see a variable called t in there anywhere? That line you copied is an evaluation of the function at the time t = 0.

The equation is W = 160 gallons - (7 gallons/hr)*t

My suggestion is that you get some sleep, and look at it again in the morning.

Answer 18

ok thank you and sorry for not being able to understand the problem, Thank you for your help=) @whpalmer4

Answer 19

You're welcome. Tomorrow's another day...fresh eyes often bring fresh insight.

Answer 20

g(t) = 160 - 7t

Answer 21

t = number of hours of constant drainage

Answer 22

Thank you very much hero @Hero

Answer 23

No need to torture the students @whpalmer4