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

The three rates of production are 0.5 barrels/min , 0.33 barrels/min & 0.25 barrels/min.

Lets consider the ans choices:

total no of barrels produced in

A) 2 hrs = 60+40+30 = 130
B) 3 hrs = 90+60+45 = 195

Hence 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?

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

My attempt

Taking LCM of the 3 rates which is 12

This means in 12 minutes:
a produces 6 barrels
b produces 4 barrels
c produces 3 barrels

So after the first 12 mins total 13 barrels are produced when all a, b and c come back to starting position (notionally speaking).

Therefore 165/13 = 12 with a remainder of 9 barrels.
So total time is 12*12=144 plus the time required for 9 barrels.
If we manually check the sequence (as per the diagram) in 9 minutes 9 barrels are produced.
So total time taken for 165 barrels is 144+9=153 mins = 2 hours 33 mins

I go with option B in the current set of options.

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

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,

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

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.