Work/Rate Problem

MakeitHappen wrote:How do you go about solving this problem?

At their respective rates, pump A, B, and C can fulfill an empty tank, or pump-out the full tank in 2, 3, and 6 hours. If A and B are used to pump-out water from the half-full tank, while C is used to fill water into the tank, in how many hours, the tank will be empty?
A. 2/3
B. 1
C. 3/4
D. 3/2
E. 2

Thanks in advance!

i got C-3/4
rate of a=1/2, b=1/3,c=1/6
1/2+1/6*t-(1/2+1/3)*t=0, where 1/2-as tank is half empty, and t is time make tank empty
solving for t=3/4

MakeitHappen wrote:How do you go about solving this problem?

At their respective rates, pump A, B, and C can fulfill an empty tank, or pump-out the full tank in 2, 3, and 6 hours. If A and B are used to pump-out water from the half-full tank, while C is used to fill water into the tank, in how many hours, the tank will be empty?
A. 2/3
B. 1
C. 3/4
D. 3/2
E. 2

Thanks in advance!

I'd approach this as a distance/rate/time problem.

First, we need to convert the numbers given to rates.

If it takes someone 6 hours to do a job, then their rate of work is 1/6 of a job per hour.

So, our 3 individual rates are:

A: 1/2
B: 1/3
C: 1/6

Now that we have our individual rates, we need the combined rate of work.

Since A and B are emptying the tank, we combine their individual rates to get the "empyting" rate:

1/2 + 1/3 = 3/6 + 2/6 = 5/6

Next we have evil pump C, which is working in the opposite direction. Since C is going the wrong way, we subtract C's rate from the emptying rate:

5/6 - 1/6 = 4/6 = 2/3

Accordingly, 2/3 is the total rate at which the tank is being emptied.

Finally, we have our distance of 1/2, which is how much of the job remains (we start with a half-full tank).

So:

time = distance/rate

= (1/2)/(2/3)

= (1/2) * (3/2)

= 3/4... choose (C).

MakeitHappen wrote:How do you go about solving this problem?

At their respective rates, pump A, B, and C can fulfill an empty tank, or pump-out the full tank in 2, 3, and 6 hours. If A and B are used to pump-out water from the half-full tank, while C is used to fill water into the tank, in how many hours, the tank will be empty?
A. 2/3
B. 1
C. 3/4
D. 3/2
E. 2

Thanks in advance!

portion of tank emptied by A in 1 hr. = 1/2.
portion of tank emptied by A in 1 hr. = 1/3.
portion of tank filled by C in 1 hr. = 1/6.
So, portion of tank actually emptied in hr. = 1/2+1/3-1/6 = 2/3.
That means a full the tank would be empty in 3/2 hr.
So, a half full tank would be empty in 1/2*3/2 = 3/4 hr.