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Question

Hi, I need help with this math problem, i would understand it, but the situations are different rather than same in this rate time and total problem, so it has me confused.

The fill pipe for a tank can fill the tank in 4 h, and the drain pipe can drain the tank in 2h. If both pipes are accidentally opened, how long will it takes to empty a half-filled tank?

What has me confused here is the filling/draining situation, and the thing about a half filled tank, so if you could please explain them, that would be nice... ^-^

Answer 1

Let
t = amount of time to empty half filled tank

You have to measure the time it takes to do half a job (i.e. to empty half a tank).

If only the drain pipe was open you could drain the tank in two hours (or 1/2 the tank in 1 hour) or
t/2 of the tank in t hours

If only the fill pipe was open you could fill the tank in four hours (or 1/4 the tank in 1 hour) or
t/4 of the tank in t hours

We subtract because they are opposing each other.

t/2 - t/4 = 1/2 job (empty half the tank)
t/4 = 1/2
t = 2 hours

The half-filled tank will be empty in two hours with both pipes open.

Answer 2

Let the volume of the tank be V

Fill rate = V/ fill time = V / 4

Emptying rate = V / emptying time = V/2

Starting with a full tank - initial volume = V

Final volume = 1/2 full = V/2

Final Volume = (emptying rate - fill rate) x time
v/2 = (v/2 - v/4) x time
v/2 = (v/4) x time

Time = (v/2) / (v/4) = 2 hours

Answer 3

in other words, for every gallon of water pumped in, 2 gallons of water are pumped out

the half filled thing is like an initial barrier(call j)

essentially you need to find a question, that accounts for the rate of filling (lets say x) and the rate of removing the water (-2*x). It is negative because it is removing the water. x is the constant.

so essentially a formula for the amount of water in the tank at any given time would be something like W(x)=x+-2x+j

if you know the amount of water initially in the tank, and the amount of water that is being added in the tank, the problem can be solved.

Answer 4

Use the equation t/a + t/b = 1

So you would have t/4 + t/2 = 1

Multiply each set of numbers by 4 ( LCD )

Then you would have t + 2t = 4

3t = 4

t = 1 1/3

Answer 5

tell ur teacher ur never gonna use this
in life lol jk idk soryy