Little Texas Drilling Company has three wells, each producing oil at a

A produces 1 barrel every 2 mins so in 1 hr its 30 barrels
B produces 1 barrel in 3 mins so in 1 hr its 20 barrels
C produces 1 barrel in 4 mins so in 1 hr its 15 barrels so total in 1 hr there are 65 barrels
So in 2 hrs - 130 barrels and 3 hrs - 195 barrels

Will go with B

You can also approximate to get the answer quickly.

Well A produces 1/2 a barrel per minute.
Wells B and C produce 1/3 + 1/4 = 7/12 (a little more than half) a barrel per minute.
So all three wells combined produce a little more than 1 barrel per minute.
So for 165 barrels they will take a bit less than 165 mins which will be more than 2 hrs but less than 3 hrs.

Answer (B)

in 12 minutes
A will produce 6, B - 4 and C - 3

Total 13 in 12 minutes.

13 barrel = 12 Minutes
165 barrel = (12/13)*165 Minutes
165 Barrel = (12/13)*(165/60) Hours
165 Barrel > 2 hours

Hence Option B,

Thanks Karishma. So the answer is between 2 and 3 hours . I estimated (165*12)/13 to be roughly 150. This is right in the middle of 2 and 3, so how did you lean on 3 , which is choice B?

The way the question is worded and the options are given, you will round up.

How many hours does it take to produce 165 barrels of oil? You get 2.5 hours.
So can you say that you can produce 165 barrels in 2 hours? No.
But can you say that you can produce 165 barrels in 3 hours? Yes. Even though some extra time is left but if you will be given round number hours only, you will need 3 hours.

With the same question and same options, even if you get 2.25 hours as the actual answer, you will still say you need 3 hours (the next closest integer) since 2 hrs are not enough.

A =1/2 barrel/min
B =1/3 barrel/min
C =1/4 barrel/min

A+ B + C = 13/12 barrel/min = 65 barrel/hr

165 barrels in 3 hr hence option B

We are given that well A produces one barrel every two minutes, well B produces one barrel every three minutes, and well C produces one barrel every four minutes. Since rate = work/time, well A’s rate = 1/2, well B’s rate = 1/3, and well C’s rate = 1/4.

If we let t = the time in minutes during which the wells work together, we can create the following equation to determine t:

(1/2)t + (1/3)t + (1/4)t = 165

Multiplying the entire equation by 12, we have:

6t + 4t + 3t = 1980

13t = 1980

t = 1980/13 = 152.3 minutes

Since 152.3 minutes = 2.54 hours, the correct answer choice is B.

Alternative solution:

Since well A produces one barrel every two minutes, it can produce 30 barrels in an hour. Likewise, since well B produces one barrel every three minutes and well C produces one barrel every four minutes, they can produce 20 and 15 barrels an hour, respectively. Thus, in one hour, these 3 wells can produce 30 + 20 + 15 = 65 barrels. Thus, it takes them 165/65 = 2.54 hours to produce 165 barrels.

[Note: Something is wrong with this problem, because the exact time is 2.54 hours, which can be rounded to 3, but I think they really want the answer to be exactly 3. If that is the case, the total number of barrels should be 195 barrels, not 165 barrels.]

Answer: B

r=td
rA=1/2; rB=1/3; rC=1/4
rA+rB+rC(t)=165
(1/2+1/3+1/4)t=165
t=165/(6+4+3/12)
t=165/13/12 mins / 60 = hrs
t=165*12/13*60=33/13=2+7/13>2.5~(3) hrs

Ans (B)

Is this question a really 700 level question? Seems like it should be 600-700 and more skewed towards the 600 side.